Non-Homogeneous Markov Chains and Systems
Non-Homogeneous Markov Chains and Systems

Author: P.-C.G. Vassiliou

Publisher: CRC Press

Published: 2022-12-21

Total Pages: 607

ISBN-13: 135198070X

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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.

Markov Chains
Markov Chains

Author: Pierre Bremaud

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 456

ISBN-13: 1475731248

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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
Reliability and Availability Engineering

Author: Kishor S. Trivedi

Publisher: Cambridge University Press

Published: 2017-08-03

Total Pages: 729

ISBN-13: 1107099501

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

Non-negative Matrices and Markov Chains
Non-negative Matrices and Markov Chains

Author: E. Seneta

Publisher: Springer Science & Business Media

Published: 2006-07-02

Total Pages: 295

ISBN-13: 0387327924

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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
Nonhomogeneous Matrix Products

Author: D. J. Hartfiel

Publisher: World Scientific

Published: 2002

Total Pages: 236

ISBN-13: 9810246285

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Puts together much of the basic work on infinite products of matrices, providing a primary source for such work.

Lectures on the Coupling Method
Lectures on the Coupling Method

Author: Torgny Lindvall

Publisher: Courier Corporation

Published: 2012-08-15

Total Pages: 292

ISBN-13: 048615324X

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Practical and easy-to-use reference progresses from simple to advanced topics, covering, among other topics, renewal theory, Markov chains, Poisson approximation, ergodicity, and Strassen's theorem. 1992 edition.

Foundations of Average-Cost Nonhomogeneous Controlled Markov Chains
Foundations of Average-Cost Nonhomogeneous Controlled Markov Chains

Author: Xi-Ren Cao

Publisher: Springer Nature

Published: 2020-09-09

Total Pages: 120

ISBN-13: 3030566781

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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.

Non-homogeneous Random Walks
Non-homogeneous Random Walks

Author: Mikhail Menshikov

Publisher: Cambridge University Press

Published: 2016-12-22

Total Pages: 385

ISBN-13: 1316867366

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Stochastic systems provide powerful abstract models for a variety of important real-life applications: for example, power supply, traffic flow, data transmission. They (and the real systems they model) are often subject to phase transitions, behaving in one way when a parameter is below a certain critical value, then switching behaviour as soon as that critical value is reached. In a real system, we do not necessarily have control over all the parameter values, so it is important to know how to find critical points and to understand system behaviour near these points. This book is a modern presentation of the 'semimartingale' or 'Lyapunov function' method applied to near-critical stochastic systems, exemplified by non-homogeneous random walks. Applications treat near-critical stochastic systems and range across modern probability theory from stochastic billiards models to interacting particle systems. Spatially non-homogeneous random walks are explored in depth, as they provide prototypical near-critical systems.

Markov Chains and Stochastic Stability
Markov Chains and Stochastic Stability

Author: Sean Meyn

Publisher: Cambridge University Press

Published: 2009-04-02

Total Pages: 623

ISBN-13: 0521731828

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

Author: Anatoly Lisnianski

Publisher: Springer Science & Business Media

Published: 2010-08-02

Total Pages: 393

ISBN-13: 1849963207

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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.