Introduction to Stochastic Analysis and Malliavin Calculus
Published on 17. April 2014
Book
Paperback/Softback
XVII, 279 pages
978-88-7642-497-7 (ISBN)
Description
This volume presents an introductory course on differential stochastic equations and Malliavin calculus. The material of the book has grown out of 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 differential stochastic equations and their connection with parabolic problems. The third part provides 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. In this third edition several small improvements are added and a new section devoted to the differentiability of the Feynman-Kac semigroup is introduced. A considerable number of corrections and improvements have been made.
More details
Series
Edition
2014 ed.
Language
English
Place of publication
Pisa
Switzerland
Publishing group
Birkhauser Verlag AG
Target group
Primary & secondary/elementary & high school
Graduate
Illustrations
XVII, 279 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 17 mm
Weight
458 gr
ISBN-13
978-88-7642-497-7 (9788876424977)
DOI
10.1007/978-88-7642-499-1
Schweitzer Classification
Other editions
Additional editions
Giuseppe Da Prato
Introduction to Stochastic Analysis and Malliavin Calculus
E-Book
07/2014
Edizioni Della Normale
€32.09
Available for download
Person
GIUSEPPE DA PRATO was born in La Spezia in 1936. Having graduated in Physics in 1960 from the University of Rome, he became full professor of Mathematics in 1968 and taught in Rome and in Trento. Since 1979 he has been Professor of Mathematical Analysis at the Scuola Normale Superiore di Pisa.
The scientific activity of Giuseppe Da Prato concerns infinite-dimensional analysis and partial differential stochastic equations (existence, uniqueness, invariant measures, ergodicity), with applications to optimal stochastic control.
Giuseppe Da Prato is the author of 5 other books, some co-authored with other international specialists, on control theory, stochastic differential equations and infinite dimensional Kolmogorov equations, and of more than 250 papers in international scientific journals.
Content
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.