Malliavin Calculus with Applications to Stochastic Partial Differential Equations
Medias
About
Malliavin calculus is a stochastic calculus of variations on the Wiener space. The main results of this theory are currently having influence on research developments at the cross section of probability and infinite-dimensional analysis. On the applied level, Malliavin calculus is used, for example, in the study by probabilistic methods of mathematical models in finance. This book presents some applications of Malliavin calculus to stochastic partial differential equations driven by Gaussian noises. The first five chapters are devoted to an introduction of the calculus itself, based on a general Gaussian space. In the last chapters of the book, recent research on regularity of the solution of stochastic partial differential equations, and the existence and smoothness of their probability laws, are discussed.
Content
- Introduction
- Integration by Parts and Absolute Continuity of Probability Laws
- Finite Dimensional Malliavin Calculus
- The Basic Operators of Malliavin Calculus
- Representation of Wiener Functionals
- _x0003_Criteria for Absolute Continuity
- Stochastic Partial Differential Equations Driven by Spatially Homogeneous Gaussian Noise
- Malliavin Regularity of Solutions of SPDE's
- Analysis of the Malliavin Matrix of Solutions of the SPDE's
- Definitions of spaces
- Bibliography.
Details
Publisher: EPFL Press English Imprint
Collection: Mathematics
Published: 22 april 2005
Edition: 1st edition
Media: Book
Pages count Book: 178
Format (in mm) Book: 160 x 240
Weight (in grammes): 560 (Book)
Language(s): English
EAN13 Book: 9782940222063
