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| modeling and analysis of stochastic systems: Modeling and Analysis of Stochastic Systems Vidyadhar G. Kulkarni, 2016-11-18 Building on the author’s more than 35 years of teaching experience, Modeling and Analysis of Stochastic Systems, Third Edition, covers the most important classes of stochastic processes used in the modeling of diverse systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. The third edition has been updated with several new applications, including the Google search algorithm in discrete time Markov chains, several examples from health care and finance in continuous time Markov chains, and square root staffing rule in Queuing models. More than 50 new exercises have been added to enhance its use as a course text or for self-study. The sequence of chapters and exercises has been maintained between editions, to enable those now teaching from the second edition to use the third edition. Rather than offer special tricks that work in specific problems, this book provides thorough coverage of general tools that enable the solution and analysis of stochastic models. After mastering the material in the text, readers will be well-equipped to build and analyze useful stochastic models for real-life situations. |
| modeling and analysis of stochastic systems: Introduction to Modeling and Analysis of Stochastic Systems V. G. Kulkarni, 2012-12-27 This book provides a self-contained review of all the relevant topics in probability theory. A software package called MAXIM, which runs on MATLAB, is made available for downloading. Vidyadhar G. Kulkarni is Professor of Operations Research at the University of North Carolina at Chapel Hill. |
| modeling and analysis of stochastic systems: Introduction to Modeling and Analysis of Stochastic Systems V. G. Kulkarni, 2010-11-03 This is an introductory-level text on stochastic modeling. It is suited for undergraduate students in engineering, operations research, statistics, mathematics, actuarial science, business management, computer science, and public policy. It employs a large number of examples to teach the students to use stochastic models of real-life systems to predict their performance, and use this analysis to design better systems. The book is devoted to the study of important classes of stochastic processes: discrete and continuous time Markov processes, Poisson processes, renewal and regenerative processes, semi-Markov processes, queueing models, and diffusion processes. The book systematically studies the short-term and the long-term behavior, cost/reward models, and first passage times. All the material is illustrated with many examples, and case studies. The book provides a concise review of probability in the appendix. The book emphasizes numerical answers to the problems. A collection of MATLAB programs to accompany the this book can be downloaded from http://www.unc.edu/~vkulkarn/Maxim/maxim.zip. A graphical user interface to access the above files can be downloaded from http://www.unc.edu/~vkulkarn/Maxim/maximgui.zip . The second edition incorporates several changes. First its title reflects the changes in content: the chapters on design and control have been removed. The book now contains several case studies that teach the design principles. Two new chapters have been added. The new chapter on Poisson processes gives more attention to this important class of stochastic processes than the first edition did. The new chapter on Brownian motion reflects its increasing importance as an appropriate model for a variety of real-life situations, including finance. |
| modeling and analysis of stochastic systems: Modeling and Analysis of Stochastic Systems, Third Edition Vidyadhar G. Kulkarni, 2016-11-18 Building on the author’s more than 35 years of teaching experience, Modeling and Analysis of Stochastic Systems, Third Edition, covers the most important classes of stochastic processes used in the modeling of diverse systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. The third edition has been updated with several new applications, including the Google search algorithm in discrete time Markov chains, several examples from health care and finance in continuous time Markov chains, and square root staffing rule in Queuing models. More than 50 new exercises have been added to enhance its use as a course text or for self-study. The sequence of chapters and exercises has been maintained between editions, to enable those now teaching from the second edition to use the third edition. Rather than offer special tricks that work in specific problems, this book provides thorough coverage of general tools that enable the solution and analysis of stochastic models. After mastering the material in the text, readers will be well-equipped to build and analyze useful stochastic models for real-life situations. |
| modeling and analysis of stochastic systems: Stochastic Modeling Barry L. Nelson, 2012-10-11 Coherent introduction to techniques also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Includes formulation of models, analysis, and interpretation of results. 1995 edition. |
| modeling and analysis of stochastic systems: Modeling and Analysis of Stochastic Systems, Second Edition Vidyadhar G. Kulkarni, 2009-12-18 Based on the author's more than 25 years of teaching experience, Modeling and Analysis of Stochastic Systems, Second Edition covers the most important classes of stochastic processes used in the modeling of diverse systems, from supply chains and inventory systems to genetics and biological systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. Along with reorganizing the material, this edition revises and adds new exercises and examples. New to the second edition: a new chapter on diffusion processes that gives an accessible and non-measure-theoretic treatment with applications to finance; a more streamlined, application-oriented approach to renewal, regenerative, and Markov regenerative processes; and, two appendices that collect relevant results from analysis and differential and difference equations. Rather than offer special tricks that work in specific problems, this book provides thorough coverage of general tools that enable the solution and analysis of stochastic models. After mastering the material in the text, students will be well-equipped to build and analyze useful stochastic models for various situations. A collection of MATLAB[registered]-based programs can be downloaded from the author's website and a solutions manual is available for qualifying instructors. |
| modeling and analysis of stochastic systems: An Introduction to Stochastic Modeling Howard M. Taylor, Samuel Karlin, 2014-05-10 An Introduction to Stochastic Modeling, Revised Edition provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful. |
| modeling and analysis of stochastic systems: Linear Stochastic Systems Anders Lindquist, Giorgio Picci, 2015-04-24 This book presents a treatise on the theory and modeling of second-order stationary processes, including an exposition on selected application areas that are important in the engineering and applied sciences. The foundational issues regarding stationary processes dealt with in the beginning of the book have a long history, starting in the 1940s with the work of Kolmogorov, Wiener, Cramér and his students, in particular Wold, and have since been refined and complemented by many others. Problems concerning the filtering and modeling of stationary random signals and systems have also been addressed and studied, fostered by the advent of modern digital computers, since the fundamental work of R.E. Kalman in the early 1960s. The book offers a unified and logically consistent view of the subject based on simple ideas from Hilbert space geometry and coordinate-free thinking. In this framework, the concepts of stochastic state space and state space modeling, based on the notion of the conditional independence of past and future flows of the relevant signals, are revealed to be fundamentally unifying ideas. The book, based on over 30 years of original research, represents a valuable contribution that will inform the fields of stochastic modeling, estimation, system identification, and time series analysis for decades to come. It also provides the mathematical tools needed to grasp and analyze the structures of algorithms in stochastic systems theory. |
| modeling and analysis of stochastic systems: Stochastic Analysis, Stochastic Systems, and Applications to Finance Allanus Hak-Man Tsoi, David Nualart, George Yin, 2011 Pt. I. Stochastic analysis and systems. 1. Multidimensional Wick-Ito formula for Gaussian processes / D. Nualart and S. Ortiz-Latorre. 2. Fractional white noise multiplication / A.H. Tsoi. 3. Invariance principle of regime-switching diffusions / C. Zhu and G. Yin -- pt. II. Finance and stochastics. 4. Real options and competition / A. Bensoussan, J.D. Diltz and S.R. Hoe. 5. Finding expectations of monotone functions of binary random variables by simulation, with applications to reliability, finance, and round robin tournaments / M. Brown, E.A. Pekoz and S.M. Ross. 6. Filtering with counting process observations and other factors : applications to bond price tick data / X. Hu, D.R. Kuipers and Y. Zeng. 7. Jump bond markets some steps towards general models in applications to hedging and utility problems / M. Kohlmann and D. Xiong. 8. Recombining tree for regime-switching model : algorithm and weak convergence / R.H. Liu. 9. Optimal reinsurance under a jump diffusion model / S. Luo. 10. Applications of counting processes and martingales in survival analysis / J. Sun. 11. Stochastic algorithms and numerics for mean-reverting asset trading / Q. Zhang, C. Zhuang and G. Yin |
| modeling and analysis of stochastic systems: Stochastic Models of Systems Vladimir S. Korolyuk, Vladimir V. Korolyuk, 2012-12-06 In this monograph stochastic models of systems analysis are discussed. It covers many aspects and different stages from the construction of mathematical models of real systems, through mathematical analysis of models based on simplification methods, to the interpretation of real stochastic systems. The stochastic models described here share the property that their evolutionary aspects develop under the influence of random factors. It has been assumed that the evolution takes place in a random medium, i.e. unilateral interaction between the system and the medium. As only Markovian models of random medium are considered in this book, the stochastic models described here are determined by two processes, a switching process describing the evolution of the systems and a switching process describing the changes of the random medium. Audience: This book will be of interest to postgraduate students and researchers whose work involves probability theory, stochastic processes, mathematical systems theory, ordinary differential equations, operator theory, or mathematical modelling and industrial mathematics. |
| modeling and analysis of stochastic systems: Introduction to Matrix Analytic Methods in Stochastic Modeling G. Latouche, V. Ramaswami, 1999-01-01 Presents the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner. |
| modeling and analysis of stochastic systems: Markov Processes for Stochastic Modeling Oliver Ibe, 2013-05-22 Markov processes are processes that have limited memory. In particular, their dependence on the past is only through the previous state. They are used to model the behavior of many systems including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. Covering a wide range of areas of application of Markov processes, this second edition is revised to highlight the most important aspects as well as the most recent trends and applications of Markov processes. The author spent over 16 years in the industry before returning to academia, and he has applied many of the principles covered in this book in multiple research projects. Therefore, this is an applications-oriented book that also includes enough theory to provide a solid ground in the subject for the reader. - Presents both the theory and applications of the different aspects of Markov processes - Includes numerous solved examples as well as detailed diagrams that make it easier to understand the principle being presented - Discusses different applications of hidden Markov models, such as DNA sequence analysis and speech analysis. |
| modeling and analysis of stochastic systems: Applied Stochastic System Modeling Shunji Osaki, 2011-12-16 This book was written for an introductory one-semester or two-quarter course in stochastic processes and their applications. The reader is assumed to have a basic knowledge of analysis and linear algebra at an undergraduate level. Stochastic models are applied in many fields such as engineering systems, physics, biology, operations research, business, economics, psychology, and linguistics. Stochastic modeling is one of the promising kinds of modeling in applied probability theory. This book is intended to introduce basic stochastic processes: Poisson pro cesses, renewal processes, discrete-time Markov chains, continuous-time Markov chains, and Markov-renewal processes. These basic processes are introduced from the viewpoint of elementary mathematics without going into rigorous treatments. This book also introduces applied stochastic system modeling such as reliability and queueing modeling. Chapters 1 and 2 deal with probability theory, which is basic and prerequisite to the following chapters. Many important concepts of probabilities, random variables, and probability distributions are introduced. Chapter 3 develops the Poisson process, which is one of the basic and im portant stochastic processes. Chapter 4 presents the renewal process. Renewal theoretic arguments are then used to analyze applied stochastic models. Chapter 5 develops discrete-time Markov chains. Following Chapter 5, Chapter 6 deals with continuous-time Markov chains. Continuous-time Markov chains have im portant applications to queueing models as seen in Chapter 9. A one-semester course or two-quarter course consists of a brief review of Chapters 1 and 2, fol lowed in order by Chapters 3 through 6. |
| modeling and analysis of stochastic systems: Stochastic Modelling and Analysis , 1988 |
| modeling and analysis of stochastic systems: Modeling and Analysis of Stochastic Systems Second Edition - Solutions Manual Taylor & Francis Group, 2009-12-11 This practical and accessible text enables readers from engineering, business, operations research, public policy and computer science to analyze stochastic systems. Emphasizing the modeling of real-life situations with stochastic elements and analyzing the resulting stochastic model, it presents the major cases of useful stochastic processes-discrete and continuous time Markov chains, renewal processes, regenerative processes, and Markov regenerative processes. The author provides reader-friendly yet rigorous coverage. He follows a set pattern of development for each class of stochastic processes and introduces Markov chains before renewal processes, so that readers can begin modeling systems early. He demonstrates both numerical and analytical solution methods in detail and dedicates a separate chapter to queueing applications. Modeling and Analysis of Stochastic Systems includes numerous worked examples and exercises, conveniently categorized as modeling, computational, or conceptual and making difficult concepts easy to grasp. Taking a practical approach to working with stochastic models, this book helps readers to model and analyze the increasingly complex and interdependent systems made possible by recent advances. |
| modeling and analysis of stochastic systems: Applied Stochastic Modelling Byron J.T. Morgan, 2008-12-02 Highlighting modern computational methods, Applied Stochastic Modelling, Second Edition provides students with the practical experience of scientific computing in applied statistics through a range of interesting real-world applications. It also successfully revises standard probability and statistical theory. Along with an updated bibliography and |
| modeling and analysis of stochastic systems: Stochastic Systems P. R. Kumar, Pravin Varaiya, 2015-12-15 Since its origins in the 1940s, the subject of decision making under uncertainty has grown into a diversified area with application in several branches of engineering and in those areas of the social sciences concerned with policy analysis and prescription. These approaches required a computing capacity too expensive for the time, until the ability to collect and process huge quantities of data engendered an explosion of work in the area. This book provides succinct and rigorous treatment of the foundations of stochastic control; a unified approach to filtering, estimation, prediction, and stochastic and adaptive control; and the conceptual framework necessary to understand current trends in stochastic control, data mining, machine learning, and robotics.? |
| modeling and analysis of stochastic systems: Applied Stochastic Processes and Control for Jump-Diffusions Floyd B. Hanson, 2007-01-01 This self-contained, practical, entry-level text integrates the basic principles of applied mathematics, applied probability, and computational science for a clear presentation of stochastic processes and control for jump diffusions in continuous time. The author covers the important problem of controlling these systems and, through the use of a jump calculus construction, discusses the strong role of discontinuous and nonsmooth properties versus random properties in stochastic systems. |
| modeling and analysis of stochastic systems: Recent Development In Stochastic Dynamics And Stochastic Analysis Jinqiao Duan, Shunlong Luo, Caishi Wang, 2010-02-08 Stochastic dynamical systems and stochastic analysis are of great interests not only to mathematicians but also to scientists in other areas. Stochastic dynamical systems tools for modeling and simulation are highly demanded in investigating complex phenomena in, for example, environmental and geophysical sciences, materials science, life sciences, physical and chemical sciences, finance and economics.The volume reflects an essentially timely and interesting subject and offers reviews on the recent and new developments in stochastic dynamics and stochastic analysis, and also some possible future research directions. Presenting a dozen chapters of survey papers and research by leading experts in the subject, the volume is written with a wide audience in mind ranging from graduate students, junior researchers to professionals of other specializations who are interested in the subject. |
| modeling and analysis of stochastic systems: Stochastic Processes and Models in Operations Research Anbazhagan, Neelamegam, 2016-03-24 Decision-making is an important task no matter the industry. Operations research, as a discipline, helps alleviate decision-making problems through the extraction of reliable information related to the task at hand in order to come to a viable solution. Integrating stochastic processes into operations research and management can further aid in the decision-making process for industrial and management problems. Stochastic Processes and Models in Operations Research emphasizes mathematical tools and equations relevant for solving complex problems within business and industrial settings. This research-based publication aims to assist scholars, researchers, operations managers, and graduate-level students by providing comprehensive exposure to the concepts, trends, and technologies relevant to stochastic process modeling to solve operations research problems. |
| modeling and analysis of stochastic systems: Stochastic Modelling of Social Processes Andreas Diekmann, Peter Mitter, 2014-05-10 Stochastic Modelling of Social Processes provides information pertinent to the development in the field of stochastic modeling and its applications in the social sciences. This book demonstrates that stochastic models can fulfill the goals of explanation and prediction. Organized into nine chapters, this book begins with an overview of stochastic models that fulfill normative, predictive, and structural–analytic roles with the aid of the theory of probability. This text then examines the study of labor market structures using analysis of job and career mobility, which is one of the approaches taken by sociologists in research on the labor market. Other chapters consider the characteristic trends and patterns from data on divorces. This book discusses as well the two approaches of stochastic modeling of social processes, namely competing risk models and semi-Markov processes. The final chapter deals with the practical application of regression models of survival data. This book is a valuable resource for social scientists and statisticians. |
| modeling and analysis of stochastic systems: Stochastic Modelling for Systems Biology, Third Edition Darren J. Wilkinson, 2018-12-07 Since the first edition of Stochastic Modelling for Systems Biology, there have been many interesting developments in the use of likelihood-free methods of Bayesian inference for complex stochastic models. Having been thoroughly updated to reflect this, this third edition covers everything necessary for a good appreciation of stochastic kinetic modelling of biological networks in the systems biology context. New methods and applications are included in the book, and the use of R for practical illustration of the algorithms has been greatly extended. There is a brand new chapter on spatially extended systems, and the statistical inference chapter has also been extended with new methods, including approximate Bayesian computation (ABC). Stochastic Modelling for Systems Biology, Third Edition is now supplemented by an additional software library, written in Scala, described in a new appendix to the book. New in the Third Edition New chapter on spatially extended systems, covering the spatial Gillespie algorithm for reaction diffusion master equation models in 1- and 2-d, along with fast approximations based on the spatial chemical Langevin equation Significantly expanded chapter on inference for stochastic kinetic models from data, covering ABC, including ABC-SMC Updated R package, including code relating to all of the new material New R package for parsing SBML models into simulatable stochastic Petri net models New open-source software library, written in Scala, replicating most of the functionality of the R packages in a fast, compiled, strongly typed, functional language Keeping with the spirit of earlier editions, all of the new theory is presented in a very informal and intuitive manner, keeping the text as accessible as possible to the widest possible readership. An effective introduction to the area of stochastic modelling in computational systems biology, this new edition adds additional detail and computational methods that will provide a stronger foundation for the development of more advanced courses in stochastic biological modelling. |
| modeling and analysis of stochastic systems: Discrete-time Stochastic Systems Torsten Söderström, 2012-12-06 This comprehensive introduction to the estimation and control of dynamic stochastic systems provides complete derivations of key results. The second edition includes improved and updated material, and a new presentation of polynomial control and new derivation of linear-quadratic-Gaussian control. |
| modeling and analysis of stochastic systems: Bayesian Analysis of Stochastic Process Models David Insua, Fabrizio Ruggeri, Mike Wiper, 2012-04-02 Bayesian analysis of complex models based on stochastic processes has in recent years become a growing area. This book provides a unified treatment of Bayesian analysis of models based on stochastic processes, covering the main classes of stochastic processing including modeling, computational, inference, forecasting, decision making and important applied models. Key features: Explores Bayesian analysis of models based on stochastic processes, providing a unified treatment. Provides a thorough introduction for research students. Computational tools to deal with complex problems are illustrated along with real life case studies Looks at inference, prediction and decision making. Researchers, graduate and advanced undergraduate students interested in stochastic processes in fields such as statistics, operations research (OR), engineering, finance, economics, computer science and Bayesian analysis will benefit from reading this book. With numerous applications included, practitioners of OR, stochastic modelling and applied statistics will also find this book useful. |
| modeling and analysis of stochastic systems: Stochastic Discrete Event Systems Armin Zimmermann, 2009-09-02 Stochastic discrete-event systems (SDES) capture the randomness in choices due to activity delays and the probabilities of decisions. This book delivers a comprehensive overview on modeling with a quantitative evaluation of SDES. It presents an abstract model class for SDES as a pivotal unifying result and details important model classes. The book also includes nontrivial examples to explain real-world applications of SDES. |
| modeling and analysis of stochastic systems: Modeling, Analysis, Design, and Control of Stochastic Systems V. G. Kulkarni, 2014-09-01 |
| modeling and analysis of stochastic systems: Renewal Processes Kosto V. Mitov, Edward Omey, 2014-04-23 This monograph serves as an introductory text to classical renewal theory and some of its applications for graduate students and researchers in mathematics and probability theory. Renewal processes play an important part in modeling many phenomena in insurance, finance, queuing systems, inventory control and other areas. In this book, an overview of univariate renewal theory is given and renewal processes in the non-lattice and lattice case are discussed. A pre-requisite is a basic knowledge of probability theory. |
| modeling and analysis of stochastic systems: Modeling and Analysis of Stochastic Systems James R. Wilson, 2000 |
| modeling and analysis of stochastic systems: Stochastic Modeling Nicolas Lanchier, 2017-01-27 Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the gambler’s ruin chain, branching processes, symmetric random walks, and queueing systems. The third, more research-oriented part of the text, discusses special stochastic processes of interest in physics, biology, and sociology. Additional emphasis is placed on minimal models that have been used historically to develop new mathematical techniques in the field of stochastic processes: the logistic growth process, the Wright –Fisher model, Kingman’s coalescent, percolation models, the contact process, and the voter model. Further treatment of the material explains how these special processes are connected to each other from a modeling perspective as well as their simulation capabilities in C and MatlabTM. |
| modeling and analysis of stochastic systems: Stochastic Analysis of Biochemical Systems David F. Anderson, Thomas G. Kurtz, 2015-04-23 This book focuses on counting processes and continuous-time Markov chains motivated by examples and applications drawn from chemical networks in systems biology. The book should serve well as a supplement for courses in probability and stochastic processes. While the material is presented in a manner most suitable for students who have studied stochastic processes up to and including martingales in continuous time, much of the necessary background material is summarized in the Appendix. Students and Researchers with a solid understanding of calculus, differential equations and elementary probability and who are well-motivated by the applications will find this book of interest. David F. Anderson is Associate Professor in the Department of Mathematics at the University of Wisconsin and Thomas G. Kurtz is Emeritus Professor in the Departments of Mathematics and Statistics at that university. Their research is focused on probability and stochastic processes with applications in biology and other areas of science and technology. These notes are based in part on lectures given by Professor Anderson at the University of Wisconsin – Madison and by Professor Kurtz at Goethe University Frankfurt. |
| modeling and analysis of stochastic systems: Stochastic Models in Biology Narendra S. Goel, Nira Richter-Dyn, 2013-10-22 Stochastic Models in Biology describes the usefulness of the theory of stochastic process in studying biological phenomena. The book describes analysis of biological systems and experiments though probabilistic models rather than deterministic methods. The text reviews the mathematical analyses for modeling different biological systems such as the random processes continuous in time and discrete in state space. The book also discusses population growth and extinction through Malthus' law and the work of MacArthur and Wilson. The text then explains the dynamics of a population of interacting species. The book also addresses population genetics under systematic evolutionary pressures known as deterministic equations and genetic changes in a finite population known as stochastic equations. The text then turns to stochastic modeling of biological systems at the molecular level, particularly the kinetics of biochemical reactions. The book also presents various useful equations such as the differential equation for generating functions for birth and death processes. The text can prove valuable for biochemists, cellular biologists, and researchers in the medical and chemical field who are tasked to perform data analysis. |
| modeling and analysis of stochastic systems: Mathematical Models of Information and Stochastic Systems Philipp Kornreich, 2018-10-03 From ancient soothsayers and astrologists to today’s pollsters and economists, probability theory has long been used to predict the future on the basis of past and present knowledge. Mathematical Models of Information and Stochastic Systems shows that the amount of knowledge about a system plays an important role in the mathematical models used to foretell the future of the system. It explains how this known quantity of information is used to derive a system’s probabilistic properties. After an introduction, the book presents several basic principles that are employed in the remainder of the text to develop useful examples of probability theory. It examines both discrete and continuous distribution functions and random variables, followed by a chapter on the average values, correlations, and covariances of functions of variables as well as the probabilistic mathematical model of quantum mechanics. The author then explores the concepts of randomness and entropy and derives various discrete probabilities and continuous probability density functions from what is known about a particular stochastic system. The final chapters discuss information of discrete and continuous systems, time-dependent stochastic processes, data analysis, and chaotic systems and fractals. By building a range of probability distributions based on prior knowledge of the problem, this classroom-tested text illustrates how to predict the behavior of diverse systems. A solutions manual is available for qualifying instructors. |
| modeling and analysis of stochastic systems: Foundations and Methods of Stochastic Simulation Barry Nelson, 2013-01-31 This graduate-level text covers modeling, programming and analysis of simulation experiments and provides a rigorous treatment of the foundations of simulation and why it works. It introduces object-oriented programming for simulation, covers both the probabilistic and statistical basis for simulation in a rigorous but accessible manner (providing all necessary background material); and provides a modern treatment of experiment design and analysis that goes beyond classical statistics. The book emphasizes essential foundations throughout, rather than providing a compendium of algorithms and theorems and prepares the reader to use simulation in research as well as practice. The book is a rigorous, but concise treatment, emphasizing lasting principles but also providing specific training in modeling, programming and analysis. In addition to teaching readers how to do simulation, it also prepares them to use simulation in their research; no other book does this. An online solutions manual for end of chapter exercises is also provided. |
| modeling and analysis of stochastic systems: Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis György Terdik, 2012-12-06 Ninety percent of inspiration is perspiration. [31] The Wiener approach to nonlinear stochastic systems [146] permits the representation of single-valued systems with memory for which a small per turbation of the input produces a small perturbation of the output. The Wiener functional series representation contains many transfer functions to describe entirely the input-output connections. Although, theoretically, these representations are elegant, in practice it is not feasible to estimate all the finite-order transfer functions (or the kernels) from a finite sam ple. One of the most important classes of stochastic systems, especially from a statistical point of view, is the case when all the transfer functions are determined by finitely many parameters. Therefore, one has to seek a finite-parameter nonlinear model which can adequately represent non linearity in a series. Among the special classes of nonlinear models that have been studied are the bilinear processes, which have found applica tions both in econometrics and control theory; see, for example, Granger and Andersen [43] and Ruberti, et al. [4]. These bilinear processes are de fined to be linear in both input and output only, when either the input or output are fixed. The bilinear model was introduced by Granger and Andersen [43] and Subba Rao [118], [119]. Terdik [126] gave the solution of xii a lower triangular bilinear model in terms of multiple Wiener-It(') integrals and gave a sufficient condition for the second order stationarity. An impor tant. |
| modeling and analysis of stochastic systems: Stochastic Approaches for Systems Biology Mukhtar Ullah, Olaf Wolkenhauer, 2011-07-12 This textbook focuses on stochastic analysis in systems biology containing both the theory and application. While the authors provide a review of probability and random variables, subsequent notions of biochemical reaction systems and the relevant concepts of probability theory are introduced side by side. This leads to an intuitive and easy-to-follow presentation of stochastic framework for modeling subcellular biochemical systems. In particular, the authors make an effort to show how the notion of propensity, the chemical master equation and the stochastic simulation algorithm arise as consequences of the Markov property. The text contains many illustrations, examples and exercises to illustrate the ideas and methods that are introduced. Matlab code is also provided where appropriate. Additionally, the cell cycle is introduced as a more complex case study. Senior undergraduate and graduate students in mathematics and physics as well as researchers working in the area of systems biology, bioinformatics and related areas will find this text useful. |
| modeling and analysis of stochastic systems: Stochastic Modelling of Electricity and Related Markets Fred Espen Benth, Jurate Saltyte Benth, Steen Koekebakker, 2008 The markets for electricity, gas and temperature have distinctive features, which provide the focus for countless studies. For instance, electricity and gas prices may soar several magnitudes above their normal levels within a short time due to imbalances in supply and demand, yielding what is known as spikes in the spot prices. The markets are also largely influenced by seasons, since power demand for heating and cooling varies over the year. The incompleteness of the markets, due to nonstorability of electricity and temperature as well as limited storage capacity of gas, makes spot-forward hedging impossible. Moreover, futures contracts are typically settled over a time period rather than at a fixed date. All these aspects of the markets create new challenges when analyzing price dynamics of spot, futures and other derivatives.This book provides a concise and rigorous treatment on the stochastic modeling of energy markets. Ornstein?Uhlenbeck processes are described as the basic modeling tool for spot price dynamics, where innovations are driven by time-inhomogeneous jump processes. Temperature futures are studied based on a continuous higher-order autoregressive model for the temperature dynamics. The theory presented here pays special attention to the seasonality of volatility and the Samuelson effect. Empirical studies using data from electricity, temperature and gas markets are given to link theory to practice. |
| modeling and analysis of stochastic systems: Stochastic Biomathematical Models Mostafa Bachar, Jerry J. Batzel, Susanne Ditlevsen, 2012-10-19 Stochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems. Recent advances in stochastic analysis and increasing computing power facilitate the analysis of more biophysically realistic models, and this book provides researchers in computational neuroscience and stochastic systems with an overview of recent developments. Key concepts are developed in chapters written by experts in their respective fields. Topics include: one-dimensional homogeneous diffusions and their boundary behavior, large deviation theory and its application in stochastic neurobiological models, a review of mathematical methods for stochastic neuronal integrate-and-fire models, stochastic partial differential equation models in neurobiology, and stochastic modeling of spreading cortical depression. |
| modeling and analysis of stochastic systems: Stochastic Controls Jiongmin Yong, Xun Yu Zhou, 2012-12-06 As is well known, Pontryagin's maximum principle and Bellman's dynamic programming are the two principal and most commonly used approaches in solving stochastic optimal control problems. * An interesting phenomenon one can observe from the literature is that these two approaches have been developed separately and independently. Since both methods are used to investigate the same problems, a natural question one will ask is the fol lowing: (Q) What is the relationship betwccn the maximum principlc and dy namic programming in stochastic optimal controls? There did exist some researches (prior to the 1980s) on the relationship between these two. Nevertheless, the results usually werestated in heuristic terms and proved under rather restrictive assumptions, which were not satisfied in most cases. In the statement of a Pontryagin-type maximum principle there is an adjoint equation, which is an ordinary differential equation (ODE) in the (finite-dimensional) deterministic case and a stochastic differential equation (SDE) in the stochastic case. The system consisting of the adjoint equa tion, the original state equation, and the maximum condition is referred to as an (extended) Hamiltonian system. On the other hand, in Bellman's dynamic programming, there is a partial differential equation (PDE), of first order in the (finite-dimensional) deterministic case and of second or der in the stochastic case. This is known as a Hamilton-Jacobi-Bellman (HJB) equation. |
| modeling and analysis of stochastic systems: Highly Structured Stochastic Systems Peter J. Green, Nils Lid Hjort, Sylvia Richardson, 2003 Highly Structured Stochastic Systems (HSSS) is a modern strategy for building statistical models for challenging real-world problems, for computing with them, and for interpreting the resulting inferences. Complexity is handled by working up from simple local assumptions in a coherent way, and that is the key to modelling, computation, inference and interpretation; the unifying framework is that of Bayesian hierarchical models. The aim of this book is to make recent developments in HSSS accessible to a general statistical audience. Graphical modelling and Markov chain Monte Carlo (MCMC) methodology are central to the field, and in this text they are covered in depth. The chapters on graphical modelling focus on causality and its interplay with time, the role of latent variables, and on some innovative applications. Those on Monte Carlo algorithms include discussion of the impact of recent theoretical work on the evaluation of performance in MCMC, extensions to variable dimension problems, and methods for dynamic problems based on particle filters. Coverage of these underlying methodologies is balanced by substantive areas of application - in the areas of spatial statistics (with epidemiological, ecological and image analysis applications) and biology (including infectious diseases, gene mapping and evolutionary genetics). The book concludes with two topics (model criticism and Bayesian nonparametrics) that seek to challenge the parametric assumptions that otherwise underlie most HSSS models. Altogether there are 15 topics in the book, and for each there is a substantial article by a leading author in the field, and two invited commentaries that complement, extend or discuss the main article, and should be read in parallel. All authors are distinguished researchers in the field, and were active participants in an international research programme on HSSS.This is the 27th volume in the Oxford Statistical Science Series, which includes texts and monographs covering many topics of current research interest in pure and applied statistics. These texts focus on topics that have been at the forefront of research interest for several years. Other books in the series include: J.Durbin and S.J.Koopman: Time series analysis by State Space Models; Peter J. Diggle, Patrick Heagerty, Kung-Yee Liang, Scott L. Zeger: Analysis of Longitudinal Data 2/e; J.K. Lindsey: Nonlinear Models in Medical Statistics; Peter J. Green, Nils L. Hjort and Sylvia Richardson: Highly Structured Stochastic Systems; Margaret S. Pepe: Statistical Evaluation of Medical Tests. |
| modeling and analysis of stochastic systems: An Introduction to Stochastic Dynamics Jinqiao Duan, 2015-04-13 An accessible introduction for applied mathematicians to concepts and techniques for describing, quantifying, and understanding dynamics under uncertainty. |
Modelling or modeling? - WordReference Forums
Feb 28, 2007 · In the case of modeling/modelling, this amounts to a wash, since there are two possible pronunciation of modeling by a (very) naive speller. But in most other three-syllable …
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May 1, 2009 · In psychotherapy, "Modeling" is the process through which, by observing the coherence between the therapist’s words and deeds, the client vicariously learns different ways …
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Modelling or modeling? - WordReference Forums
Feb 28, 2007 · In the case of modeling/modelling, this amounts to a wash, since there are two possible pronunciation of modeling by a (very) naive speller. But in most other three-syllable …
modeling (psychotherapy) - WordReference Forums
May 1, 2009 · In psychotherapy, "Modeling" is the process through which, by observing the coherence between the therapist’s words and deeds, the client vicariously learns different ways …
3D Modelling - WordReference Forums
Nov 11, 2008 · Hey guys I was just wondering if anyone could translate 3D Modelling into Japanese for me, I wanted to say to a friend of mine "I am going to study 3D Modelling at …
cuandoquiera - WordReference Forums
Oct 6, 2008 · I am working with a textbook author who is modeling the use of the subjunctive with cualquier, quienquiera, dondequiera, etc. She is concerned that the following two sentences …
comparing it against/with | WordReference Forums
Aug 5, 2011 · The following is from an English exercise given by my son's teacher. 40% of lizard species worldwide could be extinct by 2080. Barry Sinerro reached the conclusion by taking …
creosote bush | WordReference Forums
Jan 18, 2025 · A typo? It’s creosote bush. 中文名：三齿拉瑞阿 英（外）文名：Creosote Bush 拉丁学名：Larrea tridentata
today's meeting or today meeting | WordReference Forums
Apr 10, 2020 · 1 is by far the most natural way to say it. 2 is wrong. 3 is okay, but there’s no obvious reason to spell it out like that.
Year followed by E (e.g. 2019e, 2019E) (financial reporting)
Oct 20, 2020 · Hello, Could someone tell me what the letter E tacked onto the numeral representation of a year means in a stock market report, e.g. in the following quote: "Oddo …
encamamiento de pacientes - WordReference Forums
Oct 25, 2006 · Hola a todos: Estoy traduciendo un documento sobre equipo médico, el texto en el que tengo duda es: El equipo es para pacientes en encamamiento, UCI y sala de operaciones. …
se van incorporando a | WordReference Forums
Jan 30, 2009 · Hola a todos!! Tengo que traducir esta frase pero estoy en duda: " publicar los productos que se van incorporando a la página web" Mi intento: "publish the products which …
