Non Homogeneous Markov Chains And Systems

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Non-Homogeneous Markov Chains and Systems

P.-C.G. Vassiliou
Non Homogeneous Markov Chains and Systems Book PDF

Author : P.-C.G. Vassiliou
Publisher : CRC Press
Page : 607 pages
File Size : 52,5 Mb
Release : 2022-12-21
Category : Mathematics
ISBN : 9781351980708

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Non-Homogeneous Markov Chains and Systems by P.-C.G. Vassiliou Pdf

Non-Homogeneous Markov Chains and Systems: Theory and Applications fulfills two principal goals. It is devoted to the study of non-homogeneous Markov chains in the first part, and to the evolution of the theory and applications of non-homogeneous Markov systems (populations) in the second. The book is self-contained, requiring a moderate background in basic probability theory and linear algebra, common to most undergraduate programs in mathematics, statistics, and applied probability. There are some advanced parts, which need measure theory and other advanced mathematics, but the readers are alerted to these so they may focus on the basic results. Features A broad and accessible overview of non-homogeneous Markov chains and systems Fills a significant gap in the current literature A good balance of theory and applications, with advanced mathematical details separated from the main results Many illustrative examples of potential applications from a variety of fields Suitable for use as a course text for postgraduate students of applied probability, or for self-study Potential applications included could lead to other quantitative areas The book is primarily aimed at postgraduate students, researchers, and practitioners in applied probability and statistics, and the presentation has been planned and structured in a way to provide flexibility in topic selection so that the text can be adapted to meet the demands of different course outlines. The text could be used to teach a course to students studying applied probability at a postgraduate level or for self-study. It includes many illustrative examples of potential applications, in order to be useful to researchers from a variety of fields.

Non-homogeneous Markov Chains and Systems

Panos-C. G. Vassiliou
Non homogeneous Markov Chains and Systems Book PDF

Author : Panos-C. G. Vassiliou
Publisher : C&h/CRC Press
Page : 0 pages
File Size : 42,5 Mb
Release : 2022-11
Category : Markov processes
ISBN : 1032378042

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Non-homogeneous Markov Chains and Systems by Panos-C. G. Vassiliou Pdf

Non-Homogeneous Markov Chains and Systems: Theory and Applications fulfils two principal goals. It is devoted to the study of non-homogeneous Markov chains in the first part, and to the evolution of the theory and applications of non-homogeneous Markov systems (populations) in the second. The book is self-contained, requiring a moderate background in basic probability theory and linear algebra, common to most undergraduate programs in mathematics, statistics, and applied probability. There are some advanced parts, which need measure theory and other advanced mathematics, but the reader is alerted to these so they may focus on the basic results. Features: A broad and accessible overview of non-homogeneous Markov chains and systems Fills a significant gap in the current literature A good balance of theory and applications, with advanced mathematical details separated from the main results Many illustrative examples of potential applications from a variety of fields Suitable for use as a course text for postgraduate students of applied probability, or for self-study Potential applications included could open it up to other quantitative areas The book is primarily aimed at postgraduate students, researchers and practitioners in applied probability and statistics, and the presentation has been planned and structured in a way to provide flexibility in topic selection so that the text can be adapted to meet the demands of different course outlines. The book could be used to teach a course to students studying applied probability at a postgraduate level, or for self-study. It includes many illustrative examples of potential applications, so as to be useful to researchers from a variety of fields.

Markov Chains

Pierre Bremaud
Markov Chains Book PDF

Author : Pierre Bremaud
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 43,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475731248

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Markov Chains by Pierre Bremaud Pdf

Primarily an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level, the primary objective of this book is to initiate students in the art of stochastic modelling. However it is motivated by significant applications and progressively brings the student to the borders of contemporary research. Examples are from a wide range of domains, including operations research and electrical engineering. Researchers and students in these areas as well as in physics, biology and the social sciences will find this book of interest.

Reliability and Availability Engineering

Kishor S. Trivedi,Andrea Bobbio
Reliability and Availability Engineering Book PDF

Author : Kishor S. Trivedi,Andrea Bobbio
Publisher : Cambridge University Press
Page : 729 pages
File Size : 46,8 Mb
Release : 2017-08-03
Category : Computers
ISBN : 9781107099500

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Reliability and Availability Engineering by Kishor S. Trivedi,Andrea Bobbio Pdf

Learn about the techniques used for evaluating the reliability and availability of engineered systems with this comprehensive guide.

Foundations of Average-Cost Nonhomogeneous Controlled Markov Chains

Xi-Ren Cao
Foundations of Average Cost Nonhomogeneous Controlled Markov Chains Book PDF

Author : Xi-Ren Cao
Publisher : Springer Nature
Page : 120 pages
File Size : 46,5 Mb
Release : 2020-09-09
Category : Technology & Engineering
ISBN : 9783030566784

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Foundations of Average-Cost Nonhomogeneous Controlled Markov Chains by Xi-Ren Cao Pdf

This Springer brief addresses the challenges encountered in the study of the optimization of time-nonhomogeneous Markov chains. It develops new insights and new methodologies for systems in which concepts such as stationarity, ergodicity, periodicity and connectivity do not apply. This brief introduces the novel concept of confluencity and applies a relative optimization approach. It develops a comprehensive theory for optimization of the long-run average of time-nonhomogeneous Markov chains. The book shows that confluencity is the most fundamental concept in optimization, and that relative optimization is more suitable for treating the systems under consideration than standard ideas of dynamic programming. Using confluencity and relative optimization, the author classifies states as confluent or branching and shows how the under-selectivity issue of the long-run average can be easily addressed, multi-class optimization implemented, and Nth biases and Blackwell optimality conditions derived. These results are presented in a book for the first time and so may enhance the understanding of optimization and motivate new research ideas in the area.

Local Limit Theorems for Inhomogeneous Markov Chains

Dmitry Dolgopyat,Omri M. Sarig
Local Limit Theorems for Inhomogeneous Markov Chains Book PDF

Author : Dmitry Dolgopyat,Omri M. Sarig
Publisher : Springer Nature
Page : 348 pages
File Size : 53,5 Mb
Release : 2023-07-31
Category : Mathematics
ISBN : 9783031326011

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Local Limit Theorems for Inhomogeneous Markov Chains by Dmitry Dolgopyat,Omri M. Sarig Pdf

This book extends the local central limit theorem to Markov chains whose state spaces and transition probabilities are allowed to change in time. Such chains are used to model Markovian systems depending on external time-dependent parameters. The book develops a new general theory of local limit theorems for additive functionals of Markov chains, in the regimes of local, moderate, and large deviations, and provides nearly optimal conditions for the classical expansions, as well as asymptotic corrections when these conditions fail. Applications include local limit theorems for independent but not identically distributed random variables, Markov chains in random environments, and time-dependent perturbations of homogeneous Markov chains. The inclusion of appendices with background material, numerous examples, and an account of the historical background of the subject make this self-contained book accessible to graduate students. It will also be useful for researchers in probability and ergodic theory who are interested in asymptotic behaviors, Markov chains in random environments, random dynamical systems and non-stationary systems.

Non-negative Matrices and Markov Chains

E. Seneta
Non negative Matrices and Markov Chains Book PDF

Author : E. Seneta
Publisher : Springer Science & Business Media
Page : 295 pages
File Size : 45,8 Mb
Release : 2006-07-02
Category : Mathematics
ISBN : 9780387327921

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Non-negative Matrices and Markov Chains by E. Seneta Pdf

Since its inception by Perron and Frobenius, the theory of non-negative matrices has developed enormously and is now being used and extended in applied fields of study as diverse as probability theory, numerical analysis, demography, mathematical economics, and dynamic programming, while its development is still proceeding rapidly as a branch of pure mathematics in its own right. While there are books which cover this or that aspect of the theory, it is nevertheless not uncommon for workers in one or another branch of its development to be unaware of what is known in other branches, even though there is often formal overlap. One of the purposes of this book is to relate several aspects of the theory, insofar as this is possible. The author hopes that the book will be useful to mathematicians; but in particular to the workers in applied fields, so the mathematics has been kept as simple as could be managed. The mathematical requisites for reading it are: some knowledge of real-variable theory, and matrix theory; and a little knowledge of complex-variable; the emphasis is on real-variable methods. (There is only one part of the book, the second part of 55.5, which is of rather specialist interest, and requires deeper knowledge.) Appendices provide brief expositions of those areas of mathematics needed which may be less g- erally known to the average reader.

Nonhomogeneous Matrix Products

D. J. Hartfiel
Nonhomogeneous Matrix Products Book PDF

Author : D. J. Hartfiel
Publisher : World Scientific
Page : 236 pages
File Size : 53,9 Mb
Release : 2002
Category : Mathematics
ISBN : 9789812810052

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Nonhomogeneous Matrix Products by D. J. Hartfiel Pdf

Infinite products of matrices are used in nonhomogeneous Markov chains, Markov set-chains, demographics, probabilistic automata, production and manpower systems, tomography, and fractals. More recent results have been obtained in computer design of curves and surfaces. This book puts together much of the basic work on infinite products of matrices, providing a primary source for such work. This will eliminate the rediscovery of known results in the area, and thus save considerable time for researchers who work with infinite products of matrices. In addition, two chapters are included to show how infinite products of matrices are used in graphics and in systems work. Contents: Functionals; Semigroups of Matrices; Patterned Matrices; Ergodicity; Convergence; Continuous Convergence; Paracontracting; Set Convergence; Perturbations in Matrix Sets; Graphics; Slowly Varying Products; Systems. Readership: Researchers in applied mathematics, numerical and computational mathematics, industrial engineering, chaos and dynamical systems.

Homogeneous Denumerable Markov Processes

Zhenting Hou,Qingfeng Guo
Homogeneous Denumerable Markov Processes Book PDF

Author : Zhenting Hou,Qingfeng Guo
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642681271

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Homogeneous Denumerable Markov Processes by Zhenting Hou,Qingfeng Guo Pdf

Markov processes play an important role in the study of probability theory. Homogeneous denumerable Markov processes are among the main topics in the theory and have a wide range of application in various fields of science and technology (for example, in physics, cybernetics, queuing theory and dynamical programming). This book is a detailed presentation and summary of the research results obtained by the authors in recent years. Most of the results are published for the first time. Two new methods are given: one is the minimal nonnegative solution, the second the limit transition method. With the help of these two methods, the authors solve many important problems in the framework of denumerable Markov processes.

Markov Set-Chains

Darald J. Hartfiel
Markov Set Chains Book PDF

Author : Darald J. Hartfiel
Publisher : Springer
Page : 135 pages
File Size : 40,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540687115

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Markov Set-Chains by Darald J. Hartfiel Pdf

In this study extending classical Markov chain theory to handle fluctuating transition matrices, the author develops a theory of Markov set-chains and provides numerous examples showing how that theory can be applied. Chapters are concluded with a discussion of related research. Readers who can benefit from this monograph are those interested in, or involved with, systems whose data is imprecise or that fluctuate with time. A background equivalent to a course in linear algebra and one in probability theory should be sufficient.

Finite Markov Processes and Their Applications

Marius Iosifescu
Finite Markov Processes and Their Applications Book PDF

Author : Marius Iosifescu
Publisher : Courier Corporation
Page : 305 pages
File Size : 40,7 Mb
Release : 2014-07-01
Category : Mathematics
ISBN : 9780486150581

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Finite Markov Processes and Their Applications by Marius Iosifescu Pdf

A self-contained treatment of finite Markov chains and processes, this text covers both theory and applications. Author Marius Iosifescu, vice president of the Romanian Academy and director of its Center for Mathematical Statistics, begins with a review of relevant aspects of probability theory and linear algebra. Experienced readers may start with the second chapter, a treatment of fundamental concepts of homogeneous finite Markov chain theory that offers examples of applicable models. The text advances to studies of two basic types of homogeneous finite Markov chains: absorbing and ergodic chains. A complete study of the general properties of homogeneous chains follows. Succeeding chapters examine the fundamental role of homogeneous infinite Markov chains in mathematical modeling employed in the fields of psychology and genetics; the basics of nonhomogeneous finite Markov chain theory; and a study of Markovian dependence in continuous time, which constitutes an elementary introduction to the study of continuous parameter stochastic processes.

Discrete-Time Markov Chains

George Yin,Qing Zhang
Discrete Time Markov Chains Book PDF

Author : George Yin,Qing Zhang
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 40,5 Mb
Release : 2005
Category : Business & Economics
ISBN : 038721948X

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Discrete-Time Markov Chains by George Yin,Qing Zhang Pdf

Focusing on discrete-time-scale Markov chains, the contents of this book are an outgrowth of some of the authors' recent research. The motivation stems from existing and emerging applications in optimization and control of complex hybrid Markovian systems in manufacturing, wireless communication, and financial engineering. Much effort in this book is devoted to designing system models arising from these applications, analyzing them via analytic and probabilistic techniques, and developing feasible computational algorithms so as to reduce the inherent complexity. This book presents results including asymptotic expansions of probability vectors, structural properties of occupation measures, exponential bounds, aggregation and decomposition and associated limit processes, and interface of discrete-time and continuous-time systems. One of the salient features is that it contains a diverse range of applications on filtering, estimation, control, optimization, and Markov decision processes, and financial engineering. This book will be an important reference for researchers in the areas of applied probability, control theory, operations research, as well as for practitioners who use optimization techniques. Part of the book can also be used in a graduate course of applied probability, stochastic processes, and applications.

Markov Chains

Bruno Sericola
Markov Chains Book PDF

Author : Bruno Sericola
Publisher : John Wiley & Sons
Page : 306 pages
File Size : 53,6 Mb
Release : 2013-08-05
Category : Mathematics
ISBN : 9781118731536

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Markov Chains by Bruno Sericola Pdf

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. Contents 1. Discrete-Time Markov Chains 2. Continuous-Time Markov Chains 3. Birth-and-Death Processes 4. Uniformization 5. Queues About the Authors Bruno Sericola is a Senior Research Scientist at Inria Rennes – Bretagne Atlantique in France. His main research activity is in performance evaluation of computer and communication systems, dependability analysis of fault-tolerant systems and stochastic models.

Markov Chains and Stochastic Stability

Sean Meyn,Richard L. Tweedie
Markov Chains and Stochastic Stability Book PDF

Author : Sean Meyn,Richard L. Tweedie
Publisher : Cambridge University Press
Page : 623 pages
File Size : 41,8 Mb
Release : 2009-04-02
Category : Mathematics
ISBN : 9780521731829

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Markov Chains and Stochastic Stability by Sean Meyn,Richard L. Tweedie Pdf

New up-to-date edition of this influential classic on Markov chains in general state spaces. Proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background. New commentary by Sean Meyn, including updated references, reflects developments since 1996.

Multi-state System Reliability Analysis and Optimization for Engineers and Industrial Managers

Anatoly Lisnianski,Ilia Frenkel,Yi Ding
Multi state System Reliability Analysis and Optimization for Engineers and Industrial Managers Book PDF

Author : Anatoly Lisnianski,Ilia Frenkel,Yi Ding
Publisher : Springer Science & Business Media
Page : 393 pages
File Size : 40,6 Mb
Release : 2010-08-02
Category : Technology & Engineering
ISBN : 9781849963206

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Multi-state System Reliability Analysis and Optimization for Engineers and Industrial Managers by Anatoly Lisnianski,Ilia Frenkel,Yi Ding Pdf

Multi-state System Reliability Analysis and Optimization for Engineers and Industrial Managers presents a comprehensive, up-to-date description of multi-state system (MSS) reliability as a natural extension of classical binary-state reliability. It presents all essential theoretical achievements in the field, but is also practically oriented. New theoretical issues are described, including: • combined Markov and semi-Markov processes methods, and universal generating function techniques; • statistical data processing for MSSs; • reliability analysis of aging MSSs; • methods for cost-reliability and cost-availability analysis of MSSs; and • main definitions and concepts of fuzzy MSS. Multi-state System Reliability Analysis and Optimization for Engineers and Industrial Managers also discusses life cycle cost analysis and practical optimal decision making for real world MSSs. Numerous examples are included in each section in order to illustrate mathematical tools. Besides these examples, real world MSSs (such as power generating and transmission systems, air-conditioning systems, production systems, etc.) are considered as case studies. Multi-state System Reliability Analysis and Optimization for Engineers and Industrial Managers also describes basic concepts of MSS, MSS reliability measures and tools for MSS reliability assessment and optimization. It is a self-contained study resource and does not require prior knowledge from its readers, making the book attractive for researchers as well as for practical engineers and industrial managers.