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| stochastic modeling analysis and simulation: 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. |
| stochastic modeling analysis and simulation: Stochastic Modeling Barry L. Nelson, 2010-01-01 A coherent introduction to the techniques for modeling dynamic stochastic systems, this volume also offers a guide to the mathematical, numerical, and simulation tools of systems analysis. Each chapter opens with an illustrative case study, and comprehensive presentations include formulation of models, determination of parameters, analysis, and interpretation of results. 1995 edition. |
| stochastic modeling analysis and simulation: Stochastic Simulation: Algorithms and Analysis Søren Asmussen, Peter W. Glynn, 2007-07-14 Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage. Given the wide range of examples, exercises and applications students, practitioners and researchers in probability, statistics, operations research, economics, finance, engineering as well as biology and chemistry and physics will find the book of value. |
| stochastic modeling analysis and simulation: 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. |
| stochastic modeling analysis and simulation: 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. |
| stochastic modeling analysis and simulation: Stochastic Modeling Barry L. Nelson, 1995 |
| stochastic modeling analysis and simulation: Stochastic Simulation and Monte Carlo Methods Carl Graham, Denis Talay, 2013-07-16 In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic differential equations. In particular, they review the essential properties of Itô integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view. The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations. |
| stochastic modeling analysis and simulation: 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. |
| stochastic modeling analysis and simulation: 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. |
| stochastic modeling analysis and simulation: 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. |
| stochastic modeling analysis and simulation: Stochastic Modeling of Microstructures Kazimierz Sobczyk, David J. Kirkner, 2012-12-06 A major challenge in applied mathematics and mechanics of materials is to describe various types of material microstructures. The details of the microstructure of most natural and engineered materials are usually obscure; uncertainty and randomness are the inherent features. This complexity due to material heterogeneity has not been A major challenge in applied mathematics and mechanics of materials is to describe various types of material microstructures. The details of the microstructure of most natural and engineered materials are usually obscure; uncertainty and randomness are the inherent features. This complexity due to material heterogeneity has not been adequately described by current classical models and theories. Stochastic Modeling of Microstructures presents a concise and unified presentation of the basic principles and tools for the modeling of real materials, natural and man-made, that possess complex, random heterogeneity. The book uses the language and methods of random field theory combined with the basic constructs of stochastic geometry and geometrical/spatial statistics in order to give the reader the knowledge necessary to model various types of material microstructures. The application of the theoretical constructs reviewed in the first three chapters to the analysis of empirical data via the tools of statistical inference is also discussed. The final chapters address practical aspects of specific modeling problems. Features- ú First comprehensive introduction to the comparatively new field of stochastic modeling of material microstructures ú Presentation of basic tools required from the diverse subjects of random field theory, stochastic geometry and spatial statistics ú Provides background concepts from probability theory and stochastic processes are provided ú Applications from various fields are discussed, including stochastic wave propagation and the mechanics of |
| stochastic modeling analysis and simulation: Introduction to Stochastic Processes Erhan Cinlar, 2013-02-01 This clear presentation of themost fundamental models ofrandom phenomena employsmethods that recognize computerrelatedaspects of theory. Topicsinclude probability spaces andrandom variables, expectationsand independence, Bernoulliprocesses and sums of independentrandom variables, Poisson processes, Markov chainsand processes, and renewal theory. Assuming only a backgroundin calculus, this outstanding text includes an introductionto basic stochastic processes.Reprint of the Prentice-Hall Publishers, Englewood Cliffs,New Jersey, 1975 edition. |
| stochastic modeling analysis and simulation: Stochastic Simulation Optimization For Discrete Event Systems: Perturbation Analysis, Ordinal Optimization And Beyond Chun-hung Chen, Qing-shan Jia, Loo Hay Lee, 2013-07-03 Discrete event systems (DES) have become pervasive in our daily lives. Examples include (but are not restricted to) manufacturing and supply chains, transportation, healthcare, call centers, and financial engineering. However, due to their complexities that often involve millions or even billions of events with many variables and constraints, modeling these stochastic simulations has long been a “hard nut to crack”. The advance in available computer technology, especially of cluster and cloud computing, has paved the way for the realization of a number of stochastic simulation optimization for complex discrete event systems. This book will introduce two important techniques initially proposed and developed by Professor Y C Ho and his team; namely perturbation analysis and ordinal optimization for stochastic simulation optimization, and present the state-of-the-art technology, and their future research directions. |
| stochastic modeling analysis and simulation: 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. |
| stochastic modeling analysis and simulation: Stochastic Simulation Optimization Chun-hung Chen, Loo Hay Lee, 2010 With the advance of new computing technology, simulation is becoming very popular for designing large, complex, and stochastic engineering systems, since closed-form analytical solutions generally do not exist for such problems. However, the added flexibility of simulation often creates models that are computationally intractable. Moreover, to obtain a sound statistical estimate at a specified level of confidence, a large number of simulation runs (or replications) is usually required for each design alternative. If the number of design alternatives is large, the total simulation cost can be very expensive. This book addresses the pertinent efficiency issue via smart allocation of computing resource in the simulation experiments for optimization, and aims to provide academic researchers and industrial practitioners a comprehensive coverage of OCBA approach for stochastic simulation optimization. Starting with an intuitive explanation of computing budget allocation and a discussion of its impact on optimization performance, a series of OCBA approaches developed for various problems are then presented, from the selection of the best design to optimization with multiple objectives.Finally, this book discusses the potential extension of OCBA notion to different applications such as data envelopment analysis, experiments of design, and rare-event simulation. |
| stochastic modeling analysis and simulation: Stochastic modeling , |
| stochastic modeling analysis and simulation: Systems Biology Jinzhi Lei, 2021-05-13 This book discusses the mathematical simulation of biological systems, with a focus on the modeling of gene expression, gene regulatory networks and stem cell regeneration. The diffusion of morphogens is addressed by introducing various reaction-diffusion equations based on different hypotheses concerning the process of morphogen gradient formation. The robustness of steady-state gradients is also covered through boundary value problems. The introduction gives an overview of the relevant biological concepts (cells, DNA, organism development) and provides the requisite mathematical preliminaries on continuous dynamics and stochastic modeling. A basic understanding of calculus is assumed. The techniques described in this book encompass a wide range of mechanisms, from molecular behavior to population dynamics, and the inclusion of recent developments in the literature together with first-hand results make it an ideal reference for both new students and experienced researchers in the field of systems biology and applied mathematics. |
| stochastic modeling analysis and simulation: Stochastic Analysis for Finance with Simulations Geon Ho Choe, 2016-07-22 This book is an introduction to stochastic analysis and quantitative finance; it includes both theoretical and computational methods. Topics covered are stochastic calculus, option pricing, optimal portfolio investment, and interest rate models. Also included are simulations of stochastic phenomena, numerical solutions of the Black–Scholes–Merton equation, Monte Carlo methods, and time series. Basic measure theory is used as a tool to describe probabilistic phenomena. The level of familiarity with computer programming is kept to a minimum. To make the book accessible to a wider audience, some background mathematical facts are included in the first part of the book and also in the appendices. This work attempts to bridge the gap between mathematics and finance by using diagrams, graphs and simulations in addition to rigorous theoretical exposition. Simulations are not only used as the computational method in quantitative finance, but they can also facilitate an intuitive and deeper understanding of theoretical concepts. Stochastic Analysis for Finance with Simulations is designed for readers who want to have a deeper understanding of the delicate theory of quantitative finance by doing computer simulations in addition to theoretical study. It will particularly appeal to advanced undergraduate and graduate students in mathematics and business, but not excluding practitioners in finance industry. |
| stochastic modeling analysis and simulation: Mathematical Models in Population Biology and Epidemiology Fred Brauer, Carlos Castillo-Chavez, 2013-03-09 As the world population exceeds the six billion mark, questions of population explosion, of how many people the earth can support and under which conditions, become pressing. Some of the questions and challenges raised can be addressed through the use of mathemathical models, but not all. The goal of this book is to search for a balance between simple and analyzable models and unsolvable models which are capable of addressing important questions such as these. Part I focusses on single-species simple models including those which have been used to predict the growth of human and animal population in the past. Single population models are, in some sense, the building blocks of more realistic models - the subject of Part II. Their role is fundamental to the study of ecological and demographic processes including the role of population structure and spatial heterogeneity - the subject of Part III. This book, which includes both examples and exercises, will be useful to practitioners, graduate students, and scientists working in the field. |
| stochastic modeling analysis and simulation: 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. |
| stochastic modeling analysis and simulation: 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. |
| stochastic modeling analysis and simulation: Stochastic Simulation and Applications in Finance with MATLAB Programs Huu Tue Huynh, Van Son Lai, Issouf Soumare, 2011-11-21 Stochastic Simulation and Applications in Finance with MATLAB Programs explains the fundamentals of Monte Carlo simulation techniques, their use in the numerical resolution of stochastic differential equations and their current applications in finance. Building on an integrated approach, it provides a pedagogical treatment of the need-to-know materials in risk management and financial engineering. The book takes readers through the basic concepts, covering the most recent research and problems in the area, including: the quadratic re-sampling technique, the Least Squared Method, the dynamic programming and Stratified State Aggregation technique to price American options, the extreme value simulation technique to price exotic options and the retrieval of volatility method to estimate Greeks. The authors also present modern term structure of interest rate models and pricing swaptions with the BGM market model, and give a full explanation of corporate securities valuation and credit risk based on the structural approach of Merton. Case studies on financial guarantees illustrate how to implement the simulation techniques in pricing and hedging. NOTE TO READER: The CD has been converted to URL. Go to the following website www.wiley.com/go/huyhnstochastic which provides MATLAB programs for the practical examples and case studies, which will give the reader confidence in using and adapting specific ways to solve problems involving stochastic processes in finance. |
| stochastic modeling analysis and simulation: Elements of Stochastic Modelling K. A. Borovkov, 2003 This textbook has been developed from the lecture notes for a one-semester course on stochastic modelling. It reviews the basics of probability theory and then covers the following topics: Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation. Rigorous proofs are often replaced with sketches of arguments ? with indications as to why a particular result holds, and also how it is connected with other results ? and illustrated by examples. Wherever possible, the book includes references to more specialised texts containing both proofs and more advanced material related to the topics covered. |
| stochastic modeling analysis and simulation: Stochastic Petri Nets Peter J. Haas, 2002-06-27 Written by a leading researcher this book presents an introduction to Stochastic Petri Nets covering the modeling power of the proposed SPN model, the stability conditions and the simulation methods. Its unique and well-written approach provides a timely and important addition to the literature. Appeals to a wide range of researchers in engineering, computer science, mathematics and OR. |
| stochastic modeling analysis and simulation: Stochastic Modelling and Analysis , 1988 |
| stochastic modeling analysis and simulation: Modeling Complex Living Systems Nicola Bellomo, 2007-10-05 This book develops new mathematical methods and tools to model living systems. The material it presents can be used in such real-world applications as immunology, transportation engineering, and economics. The first part of the book deals with deriving general evolution equations that can be customized to particular systems of interest in the applied sciences. The second part of the book deals with various models and applications. The book will be a valuable resource to all involved in modeling complex social systems and living matter in general. |
| stochastic modeling analysis and simulation: 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. |
| stochastic modeling analysis and simulation: Multiple-point Geostatistics Professor Gregoire Mariethoz, Jef Caers, 2014-10-16 This book provides a comprehensive introduction to multiple-point geostatistics, where spatial continuity is described using training images. Multiple-point geostatistics aims at bridging the gap between physical modelling/realism and spatio-temporal stochastic modelling. The book provides an overview of this new field in three parts. Part I presents a conceptual comparison between traditional random function theory and stochastic modelling based on training images, where random function theory is not always used. Part II covers in detail various algorithms and methodologies starting from basic building blocks in statistical science and computer science. Concepts such as non-stationary and multi-variate modeling, consistency between data and model, the construction of training images and inverse modelling are treated. Part III covers three example application areas, namely, reservoir modelling, mineral resources modelling and climate model downscaling. This book will be an invaluable reference for students, researchers and practitioners of all areas of the Earth Sciences where forecasting based on spatio-temporal data is performed. |
| stochastic modeling analysis and simulation: 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 |
| stochastic modeling analysis and simulation: Probability and Stochastic Modeling Vladimir I. Rotar, 2012-08-25 A First Course in Probability with an Emphasis on Stochastic Modeling Probability and Stochastic Modeling not only covers all the topics found in a traditional introductory probability course, but also emphasizes stochastic modeling, including Markov chains, birth-death processes, and reliability models. Unlike most undergraduate-level probability texts, the book also focuses on increasingly important areas, such as martingales, classification of dependency structures, and risk evaluation. Numerous examples, exercises, and models using real-world data demonstrate the practical possibilities and restrictions of different approaches and help students grasp general concepts and theoretical results. The text is suitable for majors in mathematics and statistics as well as majors in computer science, economics, finance, and physics. The author offers two explicit options to teaching the material, which is reflected in routes designated by special roadside markers. The first route contains basic, self-contained material for a one-semester course. The second provides a more complete exposition for a two-semester course or self-study. |
| stochastic modeling analysis and simulation: 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. |
| stochastic modeling analysis and simulation: Stochastic Dynamics in Computational Biology Stefanie Winkelmann, Christof Schütte, 2021-01-04 The aim of this book is to provide a well-structured and coherent overview of existing mathematical modeling approaches for biochemical reaction systems, investigating relations between both the conventional models and several types of deterministic-stochastic hybrid model recombinations. Another main objective is to illustrate and compare diverse numerical simulation schemes and their computational effort. Unlike related works, this book presents a broad scope in its applications, from offering a detailed introduction to hybrid approaches for the case of multiple population scales to discussing the setting of time-scale separation resulting from widely varying firing rates of reaction channels. Additionally, it also addresses modeling approaches for non well-mixed reaction-diffusion dynamics, including deterministic and stochastic PDEs and spatiotemporal master equations. Finally, by translating and incorporating complex theory to a level accessible to non-mathematicians, this book effectively bridges the gap between mathematical research in computational biology and its practical use in biological, biochemical, and biomedical systems. |
| stochastic modeling analysis and simulation: Simulation and Inference for Stochastic Differential Equations Stefano M. Iacus, 2010-11-16 This book covers a highly relevant and timely topic that is of wide interest, especially in finance, engineering and computational biology. The introductory material on simulation and stochastic differential equation is very accessible and will prove popular with many readers. While there are several recent texts available that cover stochastic differential equations, the concentration here on inference makes this book stand out. No other direct competitors are known to date. With an emphasis on the practical implementation of the simulation and estimation methods presented, the text will be useful to practitioners and students with minimal mathematical background. What’s more, because of the many R programs, the information here is appropriate for many mathematically well educated practitioners, too. |
| stochastic modeling analysis and simulation: Stochastic Hydrology and its Use in Water Resources Systems Simulation and Optimization J.B. Marco, R. Harboe, J.D. Salas, 2012-12-06 Stochastic hydrology is an essential base of water resources systems analysis, due to the inherent randomness of the input, and consequently of the results. These results have to be incorporated in a decision-making process regarding the planning and management of water systems. It is through this application that stochastic hydrology finds its true meaning, otherwise it becomes merely an academic exercise. A set of well known specialists from both stochastic hydrology and water resources systems present a synthesis of the actual knowledge currently used in real-world planning and management. The book is intended for both practitioners and researchers who are willing to apply advanced approaches for incorporating hydrological randomness and uncertainty into the simulation and optimization of water resources systems. (abstract) Stochastic hydrology is a basic tool for water resources systems analysis, due to inherent randomness of the hydrologic cycle. This book contains actual techniques in use for water resources planning and management, incorporating randomness into the decision making process. Optimization and simulation, the classical systems-analysis technologies, are revisited under up-to-date statistical hydrology findings backed by real world applications. |
| stochastic modeling analysis and simulation: Optimization of Stochastic Models Georg Ch. Pflug, 1997-10-14 Stochastic models are everywhere. In manufacturing, queuing models are used for modeling production processes, realistic inventory models are stochastic in nature. Stochastic models are considered in transportation and communication. Marketing models use stochastic descriptions of the demands and buyer's behaviors. In finance, market prices and exchange rates are assumed to be certain stochastic processes, and insurance claims appear at random times with random amounts. To each decision problem, a cost function is associated. Costs may be direct or indirect, like loss of time, quality deterioration, loss in production or dissatisfaction of customers. In decision making under uncertainty, the goal is to minimize the expected costs. However, in practically all realistic models, the calculation of the expected costs is impossible due to the model complexity. Simulation is the only practicable way of getting insight into such models. Thus, the problem of optimal decisions can be seen as getting simulation and optimization effectively combined. The field is quite new and yet the number of publications is enormous. This book does not even try to touch all work done in this area. Instead, many concepts are presented and treated with mathematical rigor and necessary conditions for the correctness of various approaches are stated. Optimization of Stochastic Models: The Interface Between Simulation and Optimization is suitable as a text for a graduate level course on Stochastic Models or as a secondary text for a graduate level course in Operations Research. |
| stochastic modeling analysis and simulation: 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 |
| stochastic modeling analysis and simulation: Modeling, Analysis, Design, and Control of Stochastic Systems V. G. Kulkarni, 2014-09-01 |
| stochastic modeling analysis and simulation: Simulation and Inference for Stochastic Processes with YUIMA Stefano M. Iacus, Nakahiro Yoshida, 2018-06-01 The YUIMA package is the first comprehensive R framework based on S4 classes and methods which allows for the simulation of stochastic differential equations driven by Wiener process, Lévy processes or fractional Brownian motion, as well as CARMA, COGARCH, and Point processes. The package performs various central statistical analyses such as quasi maximum likelihood estimation, adaptive Bayes estimation, structural change point analysis, hypotheses testing, asynchronous covariance estimation, lead-lag estimation, LASSO model selection, and so on. YUIMA also supports stochastic numerical analysis by fast computation of the expected value of functionals of stochastic processes through automatic asymptotic expansion by means of the Malliavin calculus. All models can be multidimensional, multiparametric or non parametric.The book explains briefly the underlying theory for simulation and inference of several classes of stochastic processes and then presents both simulation experiments and applications to real data. Although these processes have been originally proposed in physics and more recently in finance, they are becoming popular also in biology due to the fact the time course experimental data are now available. The YUIMA package, available on CRAN, can be freely downloaded and this companion book will make the user able to start his or her analysis from the first page. |
| stochastic modeling analysis and simulation: Simulation Modeling and Analysis Averill M. Law, 2007 Accompanying CD-ROM contains ... the Student Version of the ExpertFit distribution-fitting software.--Page 4 of cover. |
| stochastic modeling analysis and simulation: Multiscale Modeling and Analysis for Materials Simulation Weizhu Bao, Qiang Du, 2012 The Institute for Mathematical Sciences at the National University of Singapore hosted a two-month research program on Mathematical Theory and Numerical Methods for Computational Materials Simulation and Design from 1 July to 31 August 2009. As an important part of the program, tutorials and special lectures were given by leading experts in the fields for participating graduate students and junior researchers. This invaluable volume collects four expanded lecture notes with self-contained tutorials. They cover a number of aspects on multiscale modeling, analysis and simulations for problems arising from materials science including some critical components in computational prediction of materials properties such as the multiscale properties of complex materials, properties of defects, interfaces and material microstructures under different conditions, critical issues in developing efficient numerical methods and analytic frameworks for complex and multiscale materials models. This volume serves to inspire graduate students and researchers who choose to embark into original research work in these fields. |
In layman's terms: What is a stochastic process?
Oct 8, 2015 · A stochastic process is a way of representing the evolution of some situation that can be characterized mathematically (by numbers, points in a graph, etc.) over time. They are …
What's the difference between stochastic and random?
Feb 28, 2012 · The terms "stochastic variable" and "random variable" both occur in the literature and are synonymous. The latter is seen more often. Similarly "stochastic process" and …
「Stochastic」与「Random」有何区别？ - 知乎
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What are the prerequisites for stochastic calculus?
Apr 22, 2013 · -Theories of convergence of stochastic processes-Theory of continuous-time stochastic processes, Brownian motion in particular. This is all covered in volume one of …
Difference between time series and stochastic process?
Jan 30, 2011 · Basically, a stochastic process is to a time series what a random variable is to a number. The realization (the "result", the observed value) of a random variable (say, a dice …
terminology - What is the difference between stochastic calculus …
Apr 4, 2015 · Stochastic calculus is to do with mathematics that operates on stochastic processes. The best known stochastic process is the Wiener process used for modelling …
How does one interpret the meaning of a stochastic derivative?
Only the integral with respect to Brownian motion is defined in the Ito- or the Stratonovich calculus. This means that there is no "stochastic derivative", and that the notion of "velocity" is …
probability theory - What is the difference between stochastic …
Aug 1, 2020 · A stochastic process is a family of random variables indexed by some set, usually $\mathbb{Z}^{n}$ or $\mathbb{R}^{n}$. It's additional structure over random variables that let …
What is stochastic mapping? - Mathematics Stack Exchange
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
Books recommendations on stochastic analysis - Mathematics …
Feb 21, 2023 · Stochastic Calculus for Finance I: Binomial asset pricing model and Stochastic Calculus for Finance II: tochastic Calculus for Finance II: Continuous-Time Models. These two …
In layman's terms: What is a stochastic process?
Oct 8, 2015 · A stochastic process is a way of representing the evolution of some situation that can be characterized mathematically (by numbers, points in a graph, etc.) over time. They are …
What's the difference between stochastic and random?
Feb 28, 2012 · The terms "stochastic variable" and "random variable" both occur in the literature and are synonymous. The latter is seen more often. Similarly "stochastic process" and "random …
「Stochastic」与「Random」有何区别？ - 知乎
知乎，中文互联网高质量的问答社区和创作者聚集的原创内容平台，于 2011 年 1 月正式上线，以「让人们更好的分享知识、经验和见解，找到自己的解答」为品牌使命。知乎凭借认真、专业 …
What are the prerequisites for stochastic calculus?
Apr 22, 2013 · -Theories of convergence of stochastic processes-Theory of continuous-time stochastic processes, Brownian motion in particular. This is all covered in volume one of …
Difference between time series and stochastic process?
Jan 30, 2011 · Basically, a stochastic process is to a time series what a random variable is to a number. The realization (the "result", the observed value) of a random variable (say, a dice roll) …
terminology - What is the difference between stochastic calculus …
Apr 4, 2015 · Stochastic calculus is to do with mathematics that operates on stochastic processes. The best known stochastic process is the Wiener process used for modelling Brownian motion. …
How does one interpret the meaning of a stochastic derivative?
Only the integral with respect to Brownian motion is defined in the Ito- or the Stratonovich calculus. This means that there is no "stochastic derivative", and that the notion of "velocity" is …
probability theory - What is the difference between stochastic …
Aug 1, 2020 · A stochastic process is a family of random variables indexed by some set, usually $\mathbb{Z}^{n}$ or $\mathbb{R}^{n}$. It's additional structure over random variables that let …
What is stochastic mapping? - Mathematics Stack Exchange
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their …
Books recommendations on stochastic analysis - Mathematics …
Feb 21, 2023 · Stochastic Calculus for Finance I: Binomial asset pricing model and Stochastic Calculus for Finance II: tochastic Calculus for Finance II: Continuous-Time Models. These two …
