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AuthorMalliavin, Paul. author
TitleStochastic Analysis [electronic resource] / by Paul Malliavin
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997
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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

Mathematics Probabilities Mathematics Probability Theory and Stochastic Processes


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