连续鞅和布朗运动（第3版）

　　本书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年这本书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。本书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本书始终的是随机积分以及强有力的游程理论。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本书中引入的新观点的理解。另外一方面这些练习也是对本书内容的丰富和完备化。

暂缺《连续鞅和布朗运动（第3版）》作者简介

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 Variables
ChapterⅠ.Introduction
§1.Examples of Stochastic Processes.Brownian Motion
§2.Local Properties of Brownian Paths
§3.Canonical Processes and Gaussian Processes
§4.Filtrations and Stopping Times
Notes and Comments
ChapterⅡ.Martingales
§1.Definitions， Maximal Inequalities and Applications
§2.Convergence and Regularization Theorems
§3.Optional Stopping Theorem
Notes and Comments
ChapterⅢ.Markov Processes
§1.Basic Definitions
§2.Feller Processes
§3.Strong Markov Property
§4.Summary of Results on Levy Processes
Notes and Comments
ChapterⅣ.Stochastic Integration
§1.Quadratic Variations
§2.Stochastic Integrals
§3.Itos Formula and First Applications
§4.Burkholder-Davis-Gundy Inequalities
§5.Predictable Processes
Notes and Comments
ChapterⅤ.Representation of Martingales
§1.Continuous Martingales as Time-changed Brownian Motions
§2.Conformal Martingales and Planar Brownian Motion
§3.Brownian Martingales
§4.Integral Representations
Notes and Comments
ChapterⅥ.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 Problem
Notes and Comments
ChapterⅦ.Generators and Time Reversal
§1.Infinitesimal Generators.
§2.Diffusions and Ito Processes
§3.Linear Continuous Markov Processes
§4.Time Reversal and Applications
Notes and Comments
ChapterⅧ.Girsanovs Theorem and First Applications
§1.Girsanovs Theorem
§2.Application of Girsanovs Theorem to the Study of Wieners Space
§3.Functionals and Transformations of Diffusion Processes
Notes and Comments
ChapterⅨ.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 One
Notes and Comments
ChapterⅩ.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 Motion
Notes and Comments
ChapterⅪ.Bessel Processes and Ray-Knight Theorems
§1.Bessel Processes
§2.Ray-Knight Theorems
§3.Bessel Bridges
Notes and Comments
ChapterⅫ.Excursions
§1.Prerequisites on Poisson Point Processes
§2.The Excursion Process of Brownian Motion
§3.Excursions Straddling a Given Time
§4.Descriptions of Itos Measure and Applications
Notes and Comments
Chapter XIII.Limit Theorems in Distribution
§1.Convergence in Distribution
§2.Asymptotic Behavior of Additive Functionals of Brownian Motion
§3.Asymptotic Properties of Planar Brownian Motion
Notes and Comments
Appendix
§1.Gronwalls 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 Equation
Bibliography
Index of Notation
Index of Terms
Catalogue