SPD

Abstract

The Malliavin derivative, divergence operator, and the Uhlenbeck operator are extended from the traditional Gaussian setting to generalized processes. Usually, the driving random source in Malliavin calculus is assumed to be an isonormal Gaussian process on a separable Hilbert space. This process is in effect a linear combination of a countable collection of independent standard Gaussian random variables. In this talk we will discuss an extension of Malliavin calculus to nonlinear functionals of the isonormal Gaussian process as the driving random source. We will also extend the main operators of Malliavin calculus to the space of generalized random elements that arise in stochastic PDEs of various types.