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Markov Processes, Structure and Asymptotic Behavior Structure and Asymptotic Behavior

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....

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Bibliographic Details
Main Author: Rosenblatt, Murray
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1971, 1971
Edition:1st ed. 1971
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
Subjects:
Applications Of Mathematics
Mathematics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I Basic Notions and Illustrations
  • 0. Summary
  • 1. Markov Processes and Transition Probability Functions
  • 2. Markov Chains
  • 3. Independent Random Variables
  • 4. Some Continuous Parameter Markov Processes
  • 5. Random Walks on Countable Commutative Groups
  • Notes
  • II Remarks on Some Applications
  • 0. Summary
  • 1. A Model in Statistical Mechanics
  • 2. Some Models in Learning Theory
  • 3. A Resource Flow Model
  • Notes
  • III Functions of Markov Processes
  • 0. Summary
  • 1. Collapsing of States and the Chapman-Kolmogorov Equation
  • 2. Markovian Functions of Markov Processes
  • 3. Functions of Finite State Markov Chains
  • Notes
  • IV Ergodic and Prediction Problems
  • 0. Summary
  • 1. A Markov Process Restricted to a Set A
  • 2. An L1 Ergodic Theorem
  • 3. Transition Operators and Invariant Measures on a Topological Space
  • 4. Asymptotic Behavior of Powers of a Transition Probability Operator
  • Notes
  • V Random Walks and Convolution on Groups and Semigroups
  • Postscript
  • Author Index
  • Notation
  • 0. Summary
  • 1. A Problem of P. Lévy
  • 2. Limit Theorems and the Convolution Operation
  • 3. Idempotent Measures as Limiting Distributions
  • 4. The Structure of Compact Semigroups
  • 5. Convergent Convolution Sequences
  • Notes
  • VI Nonlinear Representations in Terms of Independent Random Variables
  • 0. Summary
  • 1. The Linear Prediction Problem for Stationary Sequences
  • 2. A Nonlinear Prediction Problem
  • 3. Questions for Markov Processes
  • 4. Finite State Markov Chains
  • 5. Real-Valued Markov Processes
  • Notes
  • VII Mixing and the Central Limit Theorem
  • 0. Summary
  • 1. Independence
  • 2. Uniform Ergodicity, Strong Mixing and the Central Limit Problem
  • 3. An Operator Formulation of Strong Mixing and Uniform Ergodicity
  • 4. Lp Norm Conditions and a Central Limit Theorem
  • Notes
  • Appendix 1. Probability Theory
  • Appendix 2.Topological Spaces
  • Appendix 3. The Kolmogorov Extension Theorem
  • Appendix 4. Spaces and Operators
  • Appendix 5. Topological Groups

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