发表于2024-11-05
連續鞅和布朗運動 第3版 9787506291934 pdf epub mobi txt 電子書 下載 2024
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
編輯推薦
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
作者介紹
文摘
序言
連續鞅和布朗運動 第3版 9787506291934 pdf epub mobi txt 電子書 下載