馬爾可夫鏈和隨機(jī)穩(wěn)定性

內(nèi)容概要

Books are individual and idiosyncratic. In trying to understand what makes a good book, there is a limited amount that one can learn from other books; but at least one can read their prefaces, in hope of help. Our own research shows that authors use prefaces for many different reasons. Prefaces can be explanations of the role and the contents of the book, as in Chung [49] or Revuz [223] or Nummelin [202]; this can be combined with what is almost an apology for bothering the reader, as in BiUingsley [25] or Cinlar [40]; prefaces can describe the mathematics, as in Orey [208], or the importance of the applications, as in Tong [267] or Asmussen [10], or the way in which the book works as a text, as in Brockwell and Davis [32] or Revuz [223]; they can be the only available outlet for thanking those who made the task of writing possible, as in almost all of the above (although we particularly like the familial gratitude of Resnick [222] and the dedication of Simmons [240]); they can combine all these roles, and many more.

書籍目錄

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 ModeⅡ STABILITY STRUCTURES  8 Transience and Recurrence  9 Harris and Topological Recurrence  10 The Existence of π  11 Drift and Regularity  12 Invariance and TightnessⅢ 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 CriteriaIV APPENDICES  A mud Maps  B Testing for Stability  C A Glossary of Model Assumptions  D Some Mathematical BackgroundReferencesIndexSymbols Index

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