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Markov processes; structure and asymptotic behavior.

Author: Murray Rosenblatt
Publisher: Berlin, New York, Springer-Verlag, 1971.
Series: Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Bd. 184.
Edition/Format:   Print book : EnglishView all editions and formats
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Additional Physical Format: Online version:
Rosenblatt, Murray.
Markov processes.
Berlin, New York, Springer-Verlag, 1971
(OCoLC)904189807
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Murray Rosenblatt
ISBN: 0387054804 9780387054803 3540054804 9783540054801
OCLC Number: 208880
Description: xiii, 268 pages 24 cm.
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. Levy.- 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.
Series Title: Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Bd. 184.

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