基本信息

書名：連續鞅和布朗運動 第3版

定價：69.00元

作者：瑞韋茲 (Revuz.D)

齣版社：世界圖書齣版公司

齣版日期：2008-03-01

ISBN：9787506291934

字數：

頁碼：

版次：1

裝幀：平裝

開本：24開

商品重量：0.740kg

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內容提要

　　《連續鞅和布朗運動》是一部很經典的講述過程及布朗運動的教材（全英文版）。其旨在盡可能詳細的嚮概率專傢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《連續鞅和布朗運動》的版本問世以來，有關布朗運動和相關的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於它的研究，新的版本也就應運而生。《連續鞅和布朗運動》在章引入布朗運動後，以後的各章都是具體在講述某一種特定的方法或者觀點。在這些方法中貫穿於《連續鞅和布朗運動》始終的是積分以及強有力的遊程理論。

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 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 WienersSpace

§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 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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