Introduction to stochastic analysis and Malliavin calculus
By: Giuseppe Da Prato
Series: Appunti -- 6; Appunti -- 6.
Publisher: Edizioni della Normale
Published: 2007
Place of publication: Pisa, Italy
Language: eng
Number of pages: 190
ISBN-13: 9788876423130
Subjects: Stochastic differential equations; Malliavin calculus; Équations différentielles stochastiques; Calcul de Malliavin; Malliavin-Kalkül; Stochastische Analysis; Stochastische analyse
Description: "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.
Table of contents: title: 1. Gaussian measures in Hilbert spaces; title: 2. L[superscript 2] and Sobolev spaces with respect to a Gaussian measure; title: 3. Brownian motion; title: 4. Markov property of the Brownian motion; title: 5. The Ito integral; title: 6. The Ito formula; title: 7. Stochastic differential equations; title: 8. Transition evolution operators; title: 9. Formulae of Feynman-Kac and Girsanov; title: 10. One dimensional Malliavin calculus; title: 11. Malliavin calculus in several dimensions; title: 12. Asymptotic behaviour of the transition semigroup; title: A. Conditional expectation; title: B. [lambda]-systems and [pi]-systems; title: C. Martingales; title: D. Fixed points depending on parameters.