Markov Processes, Structure and Asymptotic Behavior

1. Front Matter

   Pages I-XIII

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2. Basic Notions and Illustrations

   • Murray Rosenblatt

   Pages 1-44

3. Remarks on Some Applications

   • Murray Rosenblatt

   Pages 45-56

4. Functions of Markov Processes

   • Murray Rosenblatt

   Pages 57-78

5. Ergodic and Prediction Problems

   • Murray Rosenblatt

   Pages 79-118

6. Random Walks and Convolution on Groups and Semigroups

   • Murray Rosenblatt

   Pages 119-160

7. Nonlinear Representations in Terms of Independent Random Variables

   • Murray Rosenblatt

   Pages 161-182

8. Mixing and the Central Limit Theorem

   • Murray Rosenblatt

   Pages 183-219

9. Back Matter

   Pages 220-270

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This book is concerned with a set of related problems in probability theory that are considered in the context of Markov processes. Some of these are natural to consider, especially for Markov processes. Other problems have a broader range of validity but are convenient to pose for Markov processes. The book can be used as the basis for an interesting course on Markov processes or stationary processes. For the most part these questions are considered for discrete parameter processes, although they are also of obvious interest for continuous time parameter processes. This allows one to avoid the delicate measure theoretic questions that might arise in the continuous parameter case. There is an attempt to motivate the material in terms of applications. Many of the topics concern general questions of structure and representation of processes that have not previously been presented in book form. A set of notes comment on the many problems that are still left open and related material in the literature. It is also hoped that the book will be useful as a reference to the reader who would like an introduction to these topics as well as to the reader interested in extending and completing results of this type.

• Markov
• Markov process
• Markowscher Prozess
• Natural
• Random variable
• behavior
• form
• measure
• presentation
• probability
• probability theory
• set
• time

• University of California, San Diego, La Jolla, USA

  Murray Rosenblatt

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