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| I COMMUNICATION and REGENERATION 1 Heuristics 1.1 A Range of Markovian Environments 1.2 Basic Models in Practice 1.3 Stochastic Stability For Markov Models 1.4 Commentary 2 Markov Models 2.1 Markov Models In Time Series 2.2 Nonlinear State Space Models 2.3 Models In Control And Systems Theory 2.4 Markov Models With Regeneration Times 2.5 Commentary 3 Transition Probabilities 3.1 Defining a Markovian Process 3.2 Foundations on a Countable Space 3.3 Specific Transition Matrices 3.4 Foundations for General‘State Space Chains 3.5 Building Transition Kernels For Specific Models 3.6 Commentary 4 Irreducibility 4.1 Communication and Irreducibility:Countable Spaces 4.2 ψ-Irreductibility 4.3 ψ-Irreducibility For Random Walk Modes 4.4 -Irreducible Linear Models 4.5 Commentary 5 Pseudo-atoms 5.1 Splitting ψ-Irreducible Chains 5.2 Small Sets 5.3 Small Sets for Speciic Models 5.4 Cyclic Behavior 5.5 Petiet Sets and Sampled Chains 5.6 Commentary 6 Topology and Continuity …… 7 The Nonlinear State Space Mode Ⅱ STABILITY STRUCTURES 8 Transience and Recurrence 9 Harris and Topological Recurrence 10 The Existence of π 11 Drift and Regularity 12 Invariance and Tightness Ⅲ CONVERGENCE 13 Ergodicity 14 f-Ergodicity and f-Regularity 15 Geometric Ergodicity 16 V-Uniform Ergodicity 17 Sample Paths and Limit Theorems 18 Positivity 19 Generalized Classification Criteria IV APPENDICES A mud Maps B Testing for Stability C A Glossary of Model Assumptions D Some Mathematical Background References Index Symbols Index |
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