大偏差技术和应用(第2版)

Preface to the Second Edition Preface to the Fi
t Edition 1 Introduction 1.1 Rare Events and Large Deviatio
1.2 The Large Deviation Principle 1.3 Historical Notes and References 2 LDP for Finite Dime
ional 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 Deviatio
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 Applicatio
--The Finite Dime
ional Case 3.1 Large Deviatio
for Finite State Markov Chai
3.1.1 LDP for Additive Functiona of Markov Chai
3.1.2 Sanov's Theorem for the Empirical Measure of Markov Chai
3.1.3 Sanov's Theorem for the Pair Empirical Measure of Markov Chai
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 Deviatio
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 Tra
formatio
of LDPs 4.2.1 Contraction Principles 4.2.2 Exponential Approximatio
4.3 Varadhan's Integral Lemma 4.4 Bryc's Inve
e Varadhan Lemma 4.5 LDP in Topological Vector Spaces 4.5.1 A General Upper Bound 4.5.2 Convexity Co
ideratio
4.5.3 Abstract Gartner-Ellis Theorem 4.6 Large Deviatio
for Projective Limits 4.7 The LDP and Weak Convergence in Metric Spaces 4.8 Historical Notes and References 5 Sample Path Large Deviatio
5.1 Sample Path Large Deviatio
for Random Walks 5.2 Brownian Motion Sample Path Large Deviatio
5.3 Multivariate Random Walk and Brownian Sheet 5.4 Performance Analysis of DMPSK Modulation 5.5 Large Exceedances in Rd 5.6 The Freidlin-Wentzell Theory 5.7 The Problem of Diffusion Exit from a Domain 5.8 The Performance of Tracking Loops 5.8.1 An Angular Tracking Loop Analysis 5.8.2 The Analysis of Range Tracking Loops 5.9 Historical Notes and References 6 The LDP for Abstract Empirical Measures 6.1 Cramer's Theorem in Polish Spaces 6.2 Sanov's Theorem 6.3 LDP for the Empirical Measure---The Uniform Markov Case 6.4 Mixing Conditio
and LDP 6.4.1 LDP for the Empirical Mean in Rd 6.4.2 Empirical Measure LDP for Mixing Processes 6.5 LDP for Empirical Measures of Markov Chai
6.5.1 LDP for Occupation Times 6.5.2 LDP for the k-Empirical Measures 6.5.3 Process Level LDP for Markov Chai
6.6 A Weak Convergence Approach to Large Deviatio
6.7 Historical Notes and References 7 Applicatio
of Empirical Measures LDP 7.1 Unive
al Hypothesis Testing 7.1.1 A General Statement of Test Optimality 7.1.2 Independent and Identically Distributed Observatio
7.2 Sampling Without Replacement 7.3 The Gibbs Conditioning Principle 7.3.1 The Non-Interacting Case 7.3.2 The Interacting Case 7.3.3 Refinements of the Gibbs Conditioning Principle 7.4 Historical Notes and References Appendix A Convex Analysis Co
ideratio
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 Functio
C.2 Integration and Spaces of Functio
D Probability Measures on Polish Spaces D.1 Generalities D.2 Weak Topology D.3 Product Space and Relative Entropy Decompositio
E Stochastic Analysis Bibliography General Conventio
Index of Notation Index