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Birkhäuser - Birkhäuser Mathematics - Scuola Normale Superiore | Introduction to Stochastic Analysis and Malliavin Calculus

Introduction to Stochastic Analysis and Malliavin Calculus

Da Prato, Giuseppe

Originally published as volume 6 in the series: Lecture Notes (Scuola Normale Superiore)

2nd ed.

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  • About this textbook

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 Itô'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.

Content Level » Graduate

Keywords » Malliavin calculus - stochastic analysis

Related subjects » Scuola Normale Superiore

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