多维扩散过程

出版时间：1970-1  出版社：世界图书出版公司  作者：Daniel W.Stroock，S.R.S.Varadha  页数：338  

内容概要

　　《多维扩散过程》为英文版本，内容讲述了多维物体的扩散过程，讲解详细，易懂。

作者简介

作者：(美国)Daniel W.Stroock (美国)S.R.S.Varadhan

书籍目录

Frequently Used NotationChapter 0 IntroductionChapter 1 Preliminary Material：Extension Theorems，Martingales，and Compactness1．0 Introduction1．1 Weak Convergence．Conditional Probability Distributions and Extension Theorems1．2 Martingales．1．3 The Space c([0，0)；R)1．4 Martingales and Compactness1．5 Exercises  Chapter 2 Markov Processes，Regularity of Their Sample Paths，and the Wiener Measure．2．1 Regularity of Paths2．2MarkOVProcesses andTransitionProbabilities2．3 Wiener Measure2．4 Exercises  Chapter 3 ParabolicPartialDifferentialEquations  3．1 The Maximum Principle．3．2 Existence Theorems3．3 Exercises  Chapter 4 The Stochastic Calculus of Di斤usion Theory4．1 Brownian Morion，4．2 Equivalence ofCertain Martingales4．3 It6 Processes and Stochastic Integration4．4 It’s Formula4．5 It Processes as Stochastic Integrals4．6 ExerciSes  Chapter 5 Stochastic Dilierential Equations5．0 Introduction5．1 Existence and Uniqueness5．2 On the Lipschitz Condition5．3Equivalence ofDifferentChoices ofthe SquareRoot5．4 Exercises  Chapter 6 The Martingale Formulation6．0 Introduction6．1 Existence6．2 Uniqueness：Markov Property6．3 Uniqueness：Some Examples．6．4 Cameron．Martin．Girsanov Formula6．5 Uniqueness：Random Time Change6．6 Uniqueness：Localization．6．7 Exercises  Chapter 7 Uniqueness7．0 Introduction7．1 Uniqueness：Local Case 7．2 Uniqueness：Global Case7．3 ExereiSes  Chapter 8 It’S Uniqueness and Uniqueness to the Martingale Problem8．0 Introduction．8．I Results ofYamada and Watanabe8．2 More 0n Itb Uniqueness8．3 ExercisesChapter 9 Some Estimates on the Transition Probability Functions9．0 Introduetion9．1 The Inhomogeneous Case9．2 The Homogeneous CaseChapter 10 Explosion10．0Introduction10．1 Locally Bounded Cocfficients10．2ConditionsforExplosion andNon-Explosion10．3 Exercises．Chapter 11 Limit Theorems11．0 Introduction11．1 Convergence ofDiffusion Process11．2 Convergence ofMarkov Chains to Diffusions11．3ConvergenceofDiffusionProcesses：EllipticCase11．4 Convergence ofTransition Probability Densities11．5 ExerciSeSChapter 12 The Non—Unique Case12．0 Introduction12．1 Existence ofMeasurable Choices12．2 Markov Selections12．3 Reconstruction ofAll Solutions12．4 ExercisesAppendixA．0 IntroductionA．1 L Estimates for Some Singular Integral OperatorsA．2 Proofofthe Main EstimateA．3 ExercisesBibliographical RemarksBibliographyIndex

章节摘录

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用户评论 (总计3条)

•   内容讲述了多维物体的扩散过程，讲解详细，易懂
•   这本书是扩散过程方面的经典，其实讲的就是随机微分方程，但是还提到了其它的随机微分方程书籍没有讲到的关于扩散过程的一些问题及其处理方法。
•   内容很深，需要很大勇气与毅力才能读下来~