Non-Homogeneous Markov Chains and Systems

Theory and Applications

P.-C.G. Vassiliou

• Publisher: Chapman and Hall/CRC
• Year: 2022
• ISBN:
  9781351980708
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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

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• 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.

Table of contents

• Cover Page
• Half-Title Page
• Title Page
• Copyright Page
• Dedication Page
• Contents
• Preface
• Acknowledgments
• 1 Foundations Of Probability Theory
• 2 A Small Review Of Matrix Analysis
• 3 Non-Homogeneous Markov Chains; Weak Ergodicity
• 4 Non-Homogeneous Markov Chains; Strong Ergodicity
• 5 The Non-Homogeneous Markov System
• 6 Asymptotic Behavior Of A Non-Homogeneous Markov System
• 7 Asymptotic Variability Of NHMS
• 8 Cyclic Behavior Of Non-Homogeneous Markov Systems
• 9 Stochastic Control In NHMS's
• 10 Laws Of Large Numbers For Non-Homogeneous Markov Systems
• 11 The S-NHMS In Continuous Time
• 12 The Perturbed Non-Homogeneous Markov System
• 13 Non-Homogeneous Markov Set System
• 14 Markov Systems On A General State Space
• 15 The G− Non-Homogeneous Markov System Of High Order
• References
• Index