Stochastic analysis
著者
書誌事項
Stochastic analysis
（Die Grundlehren der mathematischen Wissenschaften, 313）
Springer-Verlag, c1997
- : gw
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注記
Bibliography: p. [301]-340
Includes index
内容説明・目次
内容説明
In 5 independent sections, this book accounts 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.
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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