Malliavin Calculus with Applications to Stochastic Partial Differential Equations

ISBN: 9780849340307 出版年：2005 页码：172 Sanz-Sole, Marta EPFL Press

Introduction INTEGRATION BY PARTS AND ABSOLUTE CONTINUITY OF PROBABILITY LAWS FINITE DIMENSIONAL MALLIAVIN CALCULUS The Ornstein-Uhlenbeck Operator The Adjoint of the differential An Interration by Parts Fromula: Existence of a Density THE BASIC OPERATORS OF MALLIAVIN CALCULUS The Ornstein-Uhlenbeck Operator The Derivative Operator The Integral or Divergence Operator Differential Calculus Calculus with Multiple Wiener Intergrals Local Property of the Operators REPRESENTATION OF WIENER FUNCTIONAL The Ito Integral and the Divergence Operator The Cark-Ocone Formula Generalized Clark-Ocone Formula Application to Option Pricing CRITERIA FOR ABSOLUTE CONTINUITY AND SMOOTHNESS OF PROBABILITY LAWS Existence of a Density Smoothness of the Density STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS DRIVEN BY SPATIALLY HOMOGENEOUS GAUSSIAN NOISE Stochastic Integration with Respect to Coloured Noise Stochastic Partial Differential Equations Driven by a Coloured Noise MALLIAVIN REGULARITY OF SOLUTIONS OF SPDEs ANALYSIS OF THE MALLIAVIN MATRIC OF SOLUTIONS OF SPDEs One Dimensional Case Examples Multidimensional Case DEFINITION OF SPACES USED THROUGHOUT THE COURSE