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Introduction to stochastic analysis and Malliavin calculus / Giuseppe Da Prato.

By: Publication details: Pisa : Edizioni Della Normale, 2014.Description: xvii, 279 pISBN:
  • 9788876424977
Subject(s): DDC classification:
  • 519.23 23 P912
Contents:
Introduction.- 1 Gaussian measures in Hilbert spaces.- 2 Gaussian random variables.- 3 The Malliavin derivative.- 4 Brownian Motion.- 5 Markov property of Brownian motion.- 6 Ito's integral.- 7 Ito's formula.- 8 Stochastic differential equations.- 9 Relationship between stochastic and parabolic equations.- 10 Formulae of Feynman-Kac and Girsanov.- 11 Malliavin calculus.- 12 Asymptotic behaviour of transition semigroups.- A The Dynkin Theorem.- B Conditional expectation.- C Martingales.- D Fixed points depending on parameters.- E A basic ergodic theorem.- References.
Summary: This book introduces differential stochastic equations and Malliavin calculus. The revised and expanded third edition offers corrections and improvements and a new section covering the differentiability of the Feynman-Kac semigroup.
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Includes bibliographical references.

Introduction.-
1 Gaussian measures in Hilbert spaces.-
2 Gaussian random variables.-
3 The Malliavin derivative.-
4 Brownian Motion.-
5 Markov property of Brownian motion.-
6 Ito's integral.-
7 Ito's formula.-
8 Stochastic differential equations.-
9 Relationship between stochastic and parabolic equations.-
10 Formulae of Feynman-Kac and Girsanov.-
11 Malliavin calculus.-
12 Asymptotic behaviour of transition semigroups.-
A The Dynkin Theorem.-
B Conditional expectation.-
C Martingales.-
D Fixed points depending on parameters.-
E A basic ergodic theorem.-
References.

This book introduces differential stochastic equations and Malliavin calculus. The revised and expanded third edition offers corrections and improvements and a new section covering the differentiability of the Feynman-Kac semigroup.

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