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Stochastic Analysis

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概要 This book accounts in 5 independent parts, recent main developments of Stochastic Analysis: Gross-Stroock Sobolev space over a Gaussian probability space; quasi-sure analysis; anticipate stochastic in...tegrals as divergence operators; principle of transfer from ordinary differential equations to stochastic differential equations; Malliavin calculus and elliptic estimates; stochastic Analysis in infinite dimension.続きを見る
目次 Contents: Part I. Differential Calculus on Gaussian Probability Spaces
Ch. 1 Gaussian probability spaces
Ch. 2 Gross-Stroock Sobolev Spaces over a Gaussian Probability Space
Ch. 3 Smoothness of Laws
Part II. Quasi-Sure Analysis
Ch. 4 Foundations of Quasi-Sure Analysis: Hierarchy of Capacities and Precise Gaussian Probability Space
Ch. 5 Differential Geometry on a Precise Gaussian Probability Space
Part III. Stochastic Integrals
Ch. 6 White Noise Stochastic Integrals as Divergence
Ch. 7 Ito's Theory of Stochastic Integration
Part IV. Stochastic Differential Equations
Ch. 8 From Ordinary Differential Equations to Stochastic Flow: The Transfer Principle
Ch. 9 Elliptic Estimates through Stochastic Analysis
Part V. Stochastic Analysis in Infinite Dimensions
Ch. 10 Stochastic Analysis on Wiener Spaces
Ch. 11 Path Spaces and their Tangent Spaces
Index
Bibliography.
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登録日 2020.06.27
更新日 2020.06.28

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