连续鞅和布朗运动

作者简介

《连续鞅和布朗运动》是一部很经典的讲述随机过程及布朗运动的教材（全英文版）。其旨在尽可能详细的向概率专家介绍尽可能多的有关布朗运动的观点、技巧和方法。自从1991年这《连续鞅和布朗运动》的第一版本问世以来，有关布朗运动和相关的随机过程一直是人们研究和讨论的热点。布朗运动是许多典型的概率问题连续鞅、高斯过程、马尔科夫过程甚至更特殊的具有独立增量的过程的交叉点。大量新的方法都能够成功的应用于它的研究，新的版本也就应运而生。《连续鞅和布朗运动》在第一章引入布朗运动后，以后的各章都是具体在讲述某一种特定的方法或者观点。在这些方法中贯穿于《连续鞅和布朗运动》始终的是随机积分以及强有力的游程理论。

书籍目录

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

编辑推荐

每一部分的结束都有好多补充的练习题，一方面这些习题可以很好的帮助读者提高对这《连续鞅和布朗运动》中引入的新观点的理解。另外一方面这些练习也是对《连续鞅和布朗运动》内容的丰富和完备化。

内容概要

作者：(法国)瑞韦兹(Revuz,D)

图书封面

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