大偏差技術(shù)和應(yīng)用

內(nèi)容概要

大偏差論主要研究罕見(jiàn)事件事發(fā)概率為指數(shù)型的估計(jì)，框架由07年數(shù)學(xué)Abel獎(jiǎng)得主Varadhan于1966年引入。經(jīng)過(guò)七、八十年代Densker-Varadhan關(guān)于馬氏過(guò)程的大偏差和Freidlin-Wentzell關(guān)于動(dòng)力系統(tǒng)隨機(jī)微擾大偏差兩理論的創(chuàng)建和發(fā)展，迅速成為概率論的主流分支之一，在統(tǒng)計(jì)力學(xué)，偏微分方程動(dòng)力系統(tǒng)和分形理論，信息論，統(tǒng)計(jì)諸學(xué)科都有重要和深刻的應(yīng)用。 　　A.Dembo和O.Zeitouni所著的《大偏差技巧和應(yīng)用》第二版是國(guó)際上研究生、博士生學(xué)習(xí)大偏差理論的一本標(biāo)準(zhǔn)參考書(shū)，也是研究人員的一般標(biāo)準(zhǔn)參考書(shū)。它由淺入深，從個(gè)例到一般，從有限維到無(wú)限維，系統(tǒng)地介紹了大偏差理論的背景，思想和技巧以及大量的應(yīng)用。它內(nèi)容翔實(shí)，思想清晰，處理嚴(yán)謹(jǐn)流暢，相當(dāng)多的內(nèi)容或?yàn)樽髡咴瓌?chuàng)，或者作者從原創(chuàng)論文中摘出并加以處理。是一本非常適宜于教學(xué)和想了解和研究大偏差理論的專業(yè)人士引用最廣的大偏差理論專著。 　　本書(shū)為全英文版。

書(shū)籍目錄

Preface to the Second EditionPreface to the First Edition1 Introduction  1.1 Rare Events and Large Deviations　1.2 The Large Deviation Principle　1.3 Historical Notes and References2 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 References3 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 References4 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 References5 Sample Path Large Deviations6 The LDP for Abstract Empirical Measures7 Applications of Empirical Measures LDPAppendix　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 AnalysisBibliographyGeneral ConventionsIndex of NotationIndex

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A.Dembo和O.Zeitouni所著的《大偏差技術(shù)和應(yīng)用(第2版)》是國(guó)際上研究生、博士生學(xué)習(xí)大偏差理論的一本標(biāo)準(zhǔn)參考書(shū)，也是研究人員的一般標(biāo)準(zhǔn)參考書(shū)。《大偏差技術(shù)和應(yīng)用(第2版)》是一本非常適宜于教學(xué)和想了解和研究大偏差理論的專業(yè)人士引用最廣的大偏差理論專著。

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