Ebook: Markov Processes. Structure and Asymptotic Behavior
Author: Prof. Murray Rosenblatt (auth.)
- Tags: Mathematics general
- Series: Die Grundlehren der mathematischen Wissenschaften 184
- Year: 1971
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages I-XIII
Basic Notions and Illustrations....Pages 1-44
Remarks on Some Applications....Pages 45-56
Functions of Markov Processes....Pages 57-78
Ergodic and Prediction Problems....Pages 79-118
Random Walks and Convolution on Groups and Semigroups....Pages 119-160
Nonlinear Representations in Terms of Independent Random Variables....Pages 161-182
Mixing and the Central Limit Theorem....Pages 183-219
Back Matter....Pages 220-270
Content:
Front Matter....Pages I-XIII
Basic Notions and Illustrations....Pages 1-44
Remarks on Some Applications....Pages 45-56
Functions of Markov Processes....Pages 57-78
Ergodic and Prediction Problems....Pages 79-118
Random Walks and Convolution on Groups and Semigroups....Pages 119-160
Nonlinear Representations in Terms of Independent Random Variables....Pages 161-182
Mixing and the Central Limit Theorem....Pages 183-219
Back Matter....Pages 220-270
....