Computation of the kernels of Lévy functionals and applications

Abstract

An effective computation of the kernels of the chaos decomposition of Lévy functionals is used, to prove, among other things, a chain- and product-rule of the Malliavin derivative for a large class of Lévy processes. In case of finite and infinite-dimensional Brownian motion, the well-known rules are obtained, but for Poisson processes, the results are new. The kernels of a Lévy functional can be computed by taking the expected value of the product of this functional and multiple white noise of the Lévy process.