多維擴散過程

內(nèi)容概要

　　《多維擴散過程》為英文版本，內(nèi)容講述了多維物體的擴散過程，講解詳細，易懂。

作者簡介

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

書籍目錄

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

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