隨機(jī)分析

內(nèi)容概要

An appropriate coverage of the subjects contained in the five parts of this book would need several monographs. We hope that the global treatment presented here may emphasize some of their deep interactions. As far as possible we present self-contained proofs; we have also tried to produce a book that could be used in a graduate course.

書籍目錄

Part I. Differential Calculus on Gaussian Probability Spaces   Chapter I Gaussian Probability Spaces   Chapter II Gross-Stroock Sobolev Spaces over a Gaussian Probability Space   Chapter III Smoothness of Laws Part II. Quasi-Sure Analysis   Chapter IV Foundations of Quasi-Sure Analysis:    Hierarchy of Capacities and Precise Gaussian Probability Spaces   Chapter V Differential Geometry on a Precise Gaussian Probability Space Part III. Stochastic Integrals   Chapter VI White Noise Stochastic Integrals as Divergences   Chapter VII Ito‘s Theory of Stochastic Integration Part IV. Stochastic Differential Equations   Chapter VIII From Ordinary Differential Equations to Stochastic Flow: The Transfer Principle   Chapter IX Elliptic Estimates Through Stochastic Analysis Part V. Stochastic Analysis in Infinite Dimensions   Chapter X Stochastic Analysis on Wiener Spaces   Chapter XI Path Spaces and Their Tangent Spaces Bibliography Index Index of Notations

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