Markov Processes, Structure and Asymptotic Behavior: Structure and Asymptotic Behavior

Markov Processes, Structure and Asymptotic Behavior: Structure and Asymptotic Behavior

by Murray Rosenblatt

Paperback(Softcover reprint of the original 1st ed. 1971)

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Product Details

ISBN-13: 9783642652400
Publisher: Springer Berlin Heidelberg
Publication date: 11/11/2011
Series: Grundlehren der mathematischen Wissenschaften , #184
Edition description: Softcover reprint of the original 1st ed. 1971
Pages: 270
Product dimensions: 5.98(w) x 9.02(h) x 0.02(d)

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.- 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.- Postscript.- Author Index.- Notation.

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