Author | Rosenblatt, Murray. author |
---|---|
Title | Markov Processes. Structure and Asymptotic Behavior [electronic resource] / by Murray Rosenblatt |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1971 |
Connect to | http://dx.doi.org/10.1007/978-3-642-65238-7 |
Descript | XIV, 270 p. online resource |
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. Lรฉvy -- 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