連續(xù)鞅和布朗運動

內(nèi)容概要

　　《連續(xù)鞅和布朗運動》是一部很經(jīng)典的講述隨機過程及布朗運動的教材（全英文版）。其旨在盡可能詳細的向概率專家介紹盡可能多的有關布朗運動的觀點、技巧和方法。自從1991年這《連續(xù)鞅和布朗運動》的第一版本問世以來，有關布朗運動和相關的隨機過程一直是人們研究和討論的熱點。布朗運動是許多典型的概率問題連續(xù)鞅、高斯過程、馬爾科夫過程甚至更特殊的具有獨立增量的過程的交叉點。大量新的方法都能夠成功的應用于它的研究，新的版本也就應運而生?！哆B續(xù)鞅和布朗運動》在第一章引入布朗運動后，以后的各章都是具體在講述某一種特定的方法或者觀點。在這些方法中貫穿于《連續(xù)鞅和布朗運動》始終的是隨機積分以及強有力的游程理論。

作者簡介

作者：(法國)瑞韋茲(Revuz,D)

書籍目錄

Chapter 0.Preliminaries§1.Basic Notation§2.Monotone Class Theorem§3.Completion§4.Functions of Finite Variation and Stieltjes Integrals§5.Weak Convergence in Metric Spaces§6.Gaussian and Other Random VariablesChapterⅠ.Introduction§1.Examples of Stochastic Processes.Brownian Motion§2.Local Properties of Brownian Paths§3.Canonical Processes and Gaussian Processes§4.Filtrations and Stopping TimesNotes and CommentsChapterⅡ.Martingales§1.Definitions, Maximal Inequalities and Applications§2.Convergence and Regularization Theorems§3.Optional Stopping TheoremNotes and CommentsChapterⅢ.Markov Processes§1.Basic Definitions§2.Feller Processes§3.Strong Markov Property§4.Summary of Results on Levy ProcessesNotes and CommentsChapterⅣ.Stochastic Integration§1.Quadratic Variations§2.Stochastic Integrals§3.Ito's Formula and First Applications§4.Burkholder-Davis-Gundy Inequalities§5.Predictable ProcessesNotes and CommentsChapterⅤ.Representation of Martingales§1.Continuous Martingales as Time-changed Brownian Motions§2.Conformal Martingales and Planar Brownian Motion§3.Brownian Martingales§4.Integral RepresentationsNotes and CommentsChapterⅥ.Local Times§1.Definition and First Properties§2.The Local Time of Brownian Motion§3.The Three-Dimensional Bessel Process§4.First Order Calculus§5.The Skorokhod Stopping ProblemNotes and CommentsChapterⅦ.Generators and Time Reversal§1.Infinitesimal Generators.§2.Diffusions and Ito Processes§3.Linear Continuous Markov Processes§4.Time Reversal and ApplicationsNotes and CommentsChapterⅧ.Girsanov's Theorem and First Applications§1.Girsanov's Theorem§2.Application of Girsanov's Theorem to the Study of Wiener's Space§3.Functionals and Transformations of Diffusion ProcessesNotes and CommentsChapterⅨ.Stochastic Differential Equations§1.Formal Definitions and Uniqueness§2.Existence and Uniqueness in the Case of Lipschitz Coefficients§3.The Case of Holder Coefficients in Dimension OneNotes and CommentsChapterⅩ.Additive Functionals of Brownian Motion§1.General Definitions§2.Representation Theorem for Additive Functionals of Linear Brownian Motion§3.Ergodic Theorems for Additive Functionals§4.Asymptotic Results for the Planar Brownian MotionNotes and CommentsChapterⅪ.Bessel Processes and Ray-Knight Theorems§1.Bessel Processes§2.Ray-Knight Theorems§3.Bessel BridgesNotes and CommentsChapterⅫ.Excursions§1.Prerequisites on Poisson Point Processes§2.The Excursion Process of Brownian Motion§3.Excursions Straddling a Given Time§4.Descriptions of Ito's Measure and ApplicationsNotes and CommentsChapter XIII.Limit Theorems in Distribution§1.Convergence in Distribution§2.Asymptotic Behavior of Additive Functionals of Brownian Motion§3.Asymptotic Properties of Planar Brownian MotionNotes and CommentsAppendix§1.Gronwall's Lemma§2.Distributions§3.Convex Functions§4.Hausdorff Measures and Dimension§5.Ergodic Theory§6.Probabilities on Function Spaces§7.Bessel Functions§8.Sturm-Liouville EquationBibliographyIndex of NotationIndex of TermsCatalogue

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每一部分的結束都有好多補充的練習題，一方面這些習題可以很好的幫助讀者提高對這《連續(xù)鞅和布朗運動》中引入的新觀點的理解。另外一方面這些練習也是對《連續(xù)鞅和布朗運動》內(nèi)容的豐富和完備化。

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