Discrete Time Markov Chains
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Discrete Time Markov Chains
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Author : G. George Yin
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-10-04
Discrete Time Markov Chains written by G. George Yin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-04 with Mathematics categories.
This book focuses on two-time-scale Markov chains in discrete time. Our motivation stems from existing and emerging applications in optimization and control of complex systems in manufacturing, wireless communication, and ?nancial engineering. Much of our e?ort in this book is devoted to designing system models arising from various applications, analyzing them via analytic and probabilistic techniques, and developing feasible compu- tionalschemes. Ourmainconcernistoreducetheinherentsystemcompl- ity. Although each of the applications has its own distinct characteristics, all of them are closely related through the modeling of uncertainty due to jump or switching random processes. Oneofthesalientfeaturesofthisbookistheuseofmulti-timescalesin Markovprocessesandtheirapplications. Intuitively,notallpartsorcom- nents of a large-scale system evolve at the same rate. Some of them change rapidly and others vary slowly. The di?erent rates of variations allow us to reduce complexity via decomposition and aggregation. It would be ideal if we could divide a large system into its smallest irreducible subsystems completely separable from one another and treat each subsystem indep- dently. However, this is often infeasible in reality due to various physical constraints and other considerations. Thus, we have to deal with situations in which the systems are only nearly decomposable in the sense that there are weak links among the irreducible subsystems, which dictate the oc- sional regime changes of the system. An e?ective way to treat such near decomposability is time-scale separation. That is, we set up the systems as if there were two time scales, fast vs. slow. xii Preface Followingthetime-scaleseparation,weusesingularperturbationmeth- ology to treat the underlying systems.
Discrete Time Markov Jump Linear Systems
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Author : O.L.V. Costa
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-02-02
Discrete Time Markov Jump Linear Systems written by O.L.V. Costa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-02 with Computers categories.
This will be the most up-to-date book in the area (the closest competition was published in 1990) This book takes a new slant and is in discrete rather than continuous time
Fundamentals Of Applied Probability And Random Processes
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Author : Oliver Ibe
language : en
Publisher: Elsevier
Release Date : 2005-10-19
Fundamentals Of Applied Probability And Random Processes written by Oliver Ibe and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-19 with Mathematics categories.
This book is based on the premise that engineers use probability as a modeling tool, and that probability can be applied to the solution of engineering problems. Engineers and students studying probability and random processes also need to analyze data, and thus need some knowledge of statistics. This book is designed to provide students with a thorough grounding in probability and stochastic processes, demonstrate their applicability to real-world problems, and introduce the basics of statistics. The book's clear writing style and homework problems make it ideal for the classroom or for self-study. * Good and solid introduction to probability theory and stochastic processes * Logically organized; writing is presented in a clear manner * Choice of topics is comprehensive within the area of probability * Ample homework problems are organized into chapter sections
Understanding Markov Chains
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Author : Nicolas Privault
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-13
Understanding Markov Chains written by Nicolas Privault and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-13 with Mathematics categories.
This book provides an undergraduate introduction to discrete and continuous-time Markov chains and their applications. A large focus is placed on the first step analysis technique and its applications to average hitting times and ruin probabilities. Classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes, are also covered. Two major examples (gambling processes and random walks) are treated in detail from the beginning, before the general theory itself is presented in the subsequent chapters. An introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times is also provided, and the book includes a chapter on spatial Poisson processes with some recent results on moment identities and deviation inequalities for Poisson stochastic integrals. The concepts presented are illustrated by examples and by 72 exercises and their complete solutions.
A First Course In Stochastic Models
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Author : Henk C. Tijms
language : en
Publisher: John Wiley & Sons
Release Date : 2003-04-18
A First Course In Stochastic Models written by Henk C. Tijms and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-18 with Mathematics categories.
The field of applied probability has changed profoundly in the past twenty years. The development of computational methods has greatly contributed to a better understanding of the theory. A First Course in Stochastic Models provides a self-contained introduction to the theory and applications of stochastic models. Emphasis is placed on establishing the theoretical foundations of the subject, thereby providing a framework in which the applications can be understood. Without this solid basis in theory no applications can be solved. Provides an introduction to the use of stochastic models through an integrated presentation of theory, algorithms and applications. Incorporates recent developments in computational probability. Includes a wide range of examples that illustrate the models and make the methods of solution clear. Features an abundance of motivating exercises that help the student learn how to apply the theory. Accessible to anyone with a basic knowledge of probability. A First Course in Stochastic Models is suitable for senior undergraduate and graduate students from computer science, engineering, statistics, operations resear ch, and any other discipline where stochastic modelling takes place. It stands out amongst other textbooks on the subject because of its integrated presentation of theory, algorithms and applications.
Continuous Time Markov Processes
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Author : Thomas M. Liggett
language : en
Publisher: American Mathematical Society
Release Date : 2025-08-27
Continuous Time Markov Processes written by Thomas M. Liggett and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-27 with Mathematics categories.
Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes and applies this theory to various special examples. The initial chapter is devoted to the most important classical example?one-dimensional Brownian motion. This, together with a chapter on continuous time Markov chains, provides the motivation for the general setup based on semigroups and generators. Chapters on stochastic calculus and probabilistic potential theory give an introduction to some of the key areas of application of Brownian motion and its relatives. A chapter on interacting particle systems treats a more recently developed class of Markov processes that have as their origin problems in physics and biology. This is a textbook for a graduate course that can follow one that covers basic probabilistic limit theorems and discrete time processes.
Markov Chains
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Author : Bruno Sericola
language : en
Publisher: John Wiley & Sons
Release Date : 2013-08-05
Markov Chains written by Bruno Sericola and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-05 with Mathematics categories.
Markov Chains: Theory and Applications Markov chains are a fundamental class of stochastic processes. They are widely used to solve problems in a large number of domains such as operational research, computer science, communication networks and manufacturing systems. The success of Markov chains is mainly due to their simplicity of use, the large number of available theoretical results and the quality of algorithms developed for the numerical evaluation of many metrics of interest. The author presents the theory of both discrete-time and continuous-time homogeneous Markov chains. He carefully examines the explosion phenomenon, the Kolmogorov equations, the convergence to equilibrium and the passage time distributions to a state and to a subset of states. These results are applied to birth-and-death processes. He then proposes a detailed study of the uniformization technique by means of Banach algebra. This technique is used for the transient analysis of several queuing systems.
An Introduction To Stochastic Processes
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Author : Edward P.C. Kao
language : en
Publisher: Courier Dover Publications
Release Date : 2019-12-18
An Introduction To Stochastic Processes written by Edward P.C. Kao and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-18 with Computers categories.
This incorporation of computer use into teaching and learning stochastic processes takes an applications- and computer-oriented approach rather than a mathematically rigorous approach. Solutions Manual available to instructors upon request. 1997 edition.
Probability Models In Operations Research
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Author : C. Richard Cassady
language : en
Publisher: CRC Press
Release Date : 2008-08-05
Probability Models In Operations Research written by C. Richard Cassady and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-05 with Business & Economics categories.
Industrial engineering has expanded from its origins in manufacturing to transportation, health care, logistics, services, and more. A common denominator among all these industries, and one of the biggest challenges facing decision-makers, is the unpredictability of systems. Probability Models in Operations Research provides a comprehensive
Markov Chains
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Author : Dean L. Isaacson
language : en
Publisher: John Wiley & Sons
Release Date : 1976-03-05
Markov Chains written by Dean L. Isaacson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-03-05 with Mathematics categories.
Fundamental concepts of Markov chains; The classical approach to markov chains; The algebraic approach to Markov chains; Nonstationary Markov chains and the ergodic coeficient; Analysis of a markov chain on a computer; Continuous time Markov chains.