Stochastic Analysis (Grundlehren der mathematischen Wissenschaften) 〈Bd.313〉 （Repr.）

Malliavin, Paul

Springer（2002発売）

• 製本 Hardcover:ハードカバー版／ページ数 370 p.
• 商品コード 9783540570240

基本説明

Includes a vast bibliography of close to 800 items, and will immediately become a standard reference, indispensible to all stocastic analysts.

Full Description

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 integrals as divergence operators; principle of transfer from ordinary differential equations to stochastic differential equations; Malliavin calculus and elliptic estimates; stochastic Analysis in infinite dimension.

Contents

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.