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 |
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