Author	Malliavin, Paul. author
Title	Stochastic Analysis [electronic resource] / by Paul Malliavin
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997
Connect to	http://dx.doi.org/10.1007/978-3-642-15074-6
Descript	XII, 347 p. online resource

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: 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

1. Mathematics
2. Probabilities
3. Mathematics
4. Probability Theory and Stochastic Processes