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xvi, 190 pages ; 24 cm "This volume presents an introductory course on differential stochastic equations and Malliavin calculus. The material of the book has grown from a series of courses delivered at the Scuola Normale Superiore di Pisa (and also at the Trento and Funchal Universities) and has been refined over several years of teaching experience in the subject." "The lectures are addressed to a reader who is familiar with basic notions of measure theory and functional analysis." "The first part is devoted to the Gaussian measure in a separable Hilbert space, the Malliavin derivative, the construction of the Brownian motion and Ito's formula. The second part deals with the differential stochastic equations and their connection with parabolic problems. The third part contains an introduction to the Malliavin calculus." "Several applications are given, notably the Feynman-Kac, Girsanov and Clark-Ocone formulae, the Krylov-Bogoliubov and Von Neumann theorems."--Jacket 1. Gaussian measures in Hilbert spaces -- 2. L[superscript 2] and Sobolev spaces with respect to a Gaussian measure -- 3. Brownian motion -- 4. Markov property of the Brownian motion -- 5. The Ito integral -- 6. The I

Author

Giuseppe Da Prato

Publisher

Pisa, Italy: Edizioni della Normale

Published

2007

Language

EN

ISBN

9788876423130

Subjects

Mathematics, Stem