大偏差技术和应用（英文版）（第2版）
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作者： （美）埃米尔，（美）奥费尔著
出 版 社： 世界图书出版公司
出版时间： 2007-10-1字数：版次： 1页数： 394印刷时间： 2007/10/01开本： 24开印次： 1纸张： 胶版纸I S B N ： 9787506282918包装： 平装内容简介
大偏差论主要研究罕见事件事发概率为指数型的估计，框架由07年数学Abel奖得主Varadhan于1966年引入。经过七、八十年代Densker-Varadhan关于马氏过程的大偏差和Freidlin-Wentzell关于动力系统随机微扰大偏差两理论的创建和发展，迅速成为概率论的主流分支之一，在统计力学，偏微分方程动力系统和分形理论，信息论，统计诸学科都有重要和深刻的应用。
A.Dembo和O.Zeitouni所著的《大偏差技巧和应用》第二版是国际上研究生、博士生学习大偏差理论的一本标准参考书，也是研究人员的一般标准参考书。它由浅入深，从个例到一般，从有限维到无限维，系统地介绍了大偏差理论的背景，思想和技巧以及大量的应用。它内容翔实，思想清晰，处理严谨流畅，相当多的内容或为作者原创，或者作者从原创论文中摘出并加以处理。是一本非常适宜于教学和想了解和研究大偏差理论的专业人士引用最广的大偏差理论专著。
本书为全英文版。
目录
Preface to the Second Edition
Preface to the First Edition
1 Introduction
1.1 Rare Events and Large Deviations
1.2 The Large Deviation Principle
1.3 Historical Notes and References
2 LDP for Finite Dimensional Spaces
2.1 Combinatorial Techniques for Finite Alphabets
2.1.1 The Method of Types and Sanov's Theorem
2.1.2 Cramer's Theorem for Finite Alphabets in R
2.1.3 Large Deviations for Sampling Without Replacement
2.2 Cramer's Theorem
2.2.1 Cramer's Theorem in R
2.2.2 Cramer's Theorem in Rd
2.3 The Gartner-Ellis Theorem
2.4 Concentration Inequalities
2.4.1 Inequalities for Bounded Martingale Differences
2.4.2 Talagrand's Concentration Inequalities
2.5 Historical Notes and References
3 Applications--The Finite Dimensional Case
3.1 Large Deviations for Finite State Markov Chains
3.1.1 LDP for Additive Functiona of Markov Chains
3.1.2 Sanov's Theorem for the Empirical Measure of Markov Chains
3.1.3 Sanov's Theorem for the Pair Empirical Measure of Markov Chains
3.2 Long Rare Segments in Random Walks
3.3 The Gibbs Conditioning Principle for Finite Alphabets
3.4 The Hypothesis Testing Problem
3.5 Generalized Likelihood Ratio Test for Finite Alphabets
3.6 Rate Distortion Theory
3.7 Moderate Deviations and Exact Asymptotics in Rd
3.8 Historical Notes and References
4 General Principles
4.1 Existence of an LDP and Related Properties
4.1.1 Properties of the LDP
4.1.2 The Existence of an LDP
4.2 Transformations of LDPs
4.2.1 Contraction Principles
4.2.2 Exponential Approximations
4.3 Varadhan's Integral Lemma
4.4 Bryc's Inverse Varadhan Lemma
4.5 LDP in Topological Vector Spaces
4.5.1 A General Upper Bound
4.5.2 Convexity Considerations
4.5.3 Abstract Gartner-Ellis Theorem
4.6 Large Deviations for Projective Limits
4.7 The LDP and Weak Convergence in Metric Spaces
4.8 Historical Notes and References
5 Sample Path Large Deviations
6 The LDP for Abstract Empirical Measures
7 Applications of Empirical Measures LDP
Appendix
A Convex Analysis Considerations in Rd
B Topological Preliminaries
B.1 Generalities
B.2 Topological Vector Spaces and Weak Topologies
B.3 Banach and Polish Spaces
B.4 Mazur's Theorem
C Integration and Function Spaces
C.1 Additive Set Functions
C.2 Integration and Spaces of Functions
D Probability Measures on Polish Spaces
D.1 Generalities
D.2 Weak Topology
D.3 Product Space and Relative Entropy Decompositions
E Stochastic Analysis
Bibliography
General Conventions
Index of Notation
Index
