Large Deviations for Markov Chains

de Acosta, Alejandro D.

Large Deviations for Markov Chains
  • 出版商: Cambridge
  • 出版日期: 2022-10-27
  • 售價: $4,860
  • 貴賓價: 9.5 折 $4,617
  • 語言: 英文
  • 頁數: 262
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1316511898
  • ISBN-13: 9781316511893

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相關主題

商品描述

This book studies the large deviations for empirical measures and vector-valued additive functionals of Markov chains with general state space. Under suitable recurrence conditions, the ergodic theorem for additive functionals of a Markov chain asserts the almost sure convergence of the averages of a real or vector-valued function of the chain to the mean of the function with respect to the invariant distribution. In the case of empirical measures, the ergodic theorem states the almost sure convergence in a suitable sense to the invariant distribution. The large deviation theorems provide precise asymptotic estimates at logarithmic level of the probabilities of deviating from the preponderant behavior asserted by the ergodic theorems.

  •  
  • The first book to study large deviations for Markov chains in depth in the framework of the theory of irreducible nonnegative kernels on a general state space. The relevant aspects of this theory are presented in several appendices
  • An essential role is played by irreducibility, its consequences, and its derivative notions, such as the convergence parameter of an irreducible nonnegative kernel
  • Many results in the book have not previously appeared in the literature – this includes new results on uniformity sets and the role of invariant distributions

目錄大綱

Preface
1. Introduction
2. Lower bounds and a property of lambda
3. Upper bounds I
4. Identification and reconciliation of rate functions
5. Necessary conditions – bounds on the rate function, invariant measures, irreducibility and recurrence
6. Upper bounds II – equivalent analytic conditions
7. Upper bounds III – sufficient conditions
8. The large deviations principle for empirical measures
9. The case when S is countable and P is matrix irreducible
10. Examples
11. Large deviations for vector-valued additive functionals
Appendix A
Appendix B
Appendix C
Appendix D
Appendix E
Appendix F
Appendix G
Appendix H
Appendix I
Appendix J
Appendix K
References
Author index
Subject index.

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