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《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。

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， Mamal 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 WienersSpace

§3.Functionals and Transformations of Diffusion Processes

Notes and Comments

ChapterⅨ.Stochastic Differential Equations

§1.Formal Definitions and Uniqueness

§2.Estence and Uniqueness in the Case of LipschitzCoefficients

§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 LinearBrownian 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 BrownianMotion

§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

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书籍介绍

《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。