Large Deviations for Markov Chains
暫譯: 馬可夫鏈的大偏差理論

de Acosta, Alejandro D.

Large Deviations for Markov Chains
  • 出版商: Cambridge
  • 出版日期: 2022-10-27
  • 售價: $4,620
  • 貴賓價: 9.5 折 $4,389
  • 語言: 英文
  • 頁數: 262
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1316511898
  • ISBN-13: 9781316511893

    • 海外代購書籍(需單獨結帳)

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

商品描述(中文翻譯)

這本書研究了具有一般狀態空間的馬可夫鏈的經驗測度和向量值加法函數的巨大偏差。根據適當的重複條件，馬可夫鏈的加法函數的遍歷定理聲明，鏈的實數或向量值函數的平均值幾乎確定地收斂到相對於不變分佈的函數均值。在經驗測度的情況下，遍歷定理表示在適當的意義下幾乎確定地收斂到不變分佈。巨大偏差定理提供了在對數層面上偏離遍歷定理所聲明的主要行為的概率的精確漸近估計。

- 本書是第一本在一般狀態空間的不可約非負核理論框架下深入研究馬可夫鏈巨大偏差的書籍。該理論的相關方面在幾個附錄中呈現。
- 不可約性及其後果，以及其衍生概念（如不可約非負核的收斂參數）扮演了重要角色。
- 書中的許多結果在文獻中尚未出現過，包括有關均勻性集合和不變分佈角色的新結果。

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.

目錄大綱(中文翻譯)

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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