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Homogeneous Denumerable Markov Processes

  • Book
  • © 1988

Overview

Authors:
  1. Hou Zhenting

    1. Chang Sha Railway Institute, Chang Sha, The People’s Republic of China

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  2. Guo Qingfeng

    1. Department of Mathematics, Xiang Tan University, Xiang Tan, The People’s Republic of China

    View author publications

    You can also search for this author in PubMed   Google Scholar

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Table of contents (14 chapters)

  1. Front Matter

    Pages I-X
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  2. Construction Theory of Sample Functions of Homogeneous Denumerable Markov Processes

    1. Front Matter

      Pages 1-1
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    2. The First Construction Theorem

      • Hou Zhenting, Guo Qingfeng
      Pages 3-15

    3. The Second Construction Theorem

      • Hou Zhenting, Guo Qingfeng
      Pages 16-28

  3. Theory of Minimal Nonnegative Solutions for Systems of Nonnegative Linear Equations

    1. Front Matter

      Pages 29-29
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    2. General Theory

      • Hou Zhenting, Guo Qingfeng
      Pages 31-40

    3. Calculation

      • Hou Zhenting, Guo Qingfeng
      Pages 41-46

    4. Systems of 1-Bounded Equations

      • Hou Zhenting, Guo Qingfeng
      Pages 47-64

  4. Homogeneous Denumerable Markov Chains

    1. Front Matter

      Pages 65-65
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    2. General Theory

      • Hou Zhenting, Guo Qingfeng
      Pages 67-92

    3. Martin Exit Boundary Theory

      • Hou Zhenting, Guo Qingfeng
      Pages 93-123

    4. Martin Entrance Boundary Theory

      • Hou Zhenting, Guo Qingfeng
      Pages 124-131

  5. Homogeneous Denumerable Markov Processes

    1. Front Matter

      Pages 133-133
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    2. Minimal Q-Processes

      • Hou Zhenting, Guo Qingfeng
      Pages 135-167

    3. Q-Processes of Order One

      • Hou Zhenting, Guo Qingfeng
      Pages 168-185

    4. Arbitrary Q-Processes

      • Hou Zhenting, Guo Qingfeng
      Pages 186-199

  6. Construction Theory of Homogeneous Denumerable Markov Processes

    1. Front Matter

      Pages 201-201
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    2. Criteria for the Uniqueness of Q-Processes

      • Hou Zhenting, Guo Qingfeng
      Pages 203-239

    3. Construction of Q-Processes

      • Hou Zhenting, Guo Qingfeng
      Pages 240-245

    4. Qualitative Theory

      • Hou Zhenting, Guo Qingfeng
      Pages 246-277
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Keywords

About this book

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.

Authors and Affiliations

  • Chang Sha Railway Institute, Chang Sha, The People’s Republic of China

    Hou Zhenting

  • Department of Mathematics, Xiang Tan University, Xiang Tan, The People’s Republic of China

    Guo Qingfeng

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