COMPUTATION OF THE KERNELS OF LEVY FUNCTIONALS AND APPLICATIONS

摘要

An effective computation of the kernels of the chaos decomposition of Levy functionals is used, to prove, among other things, a chain- and product-rule of the Malliavin derivative for a large class of Levy 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 Levy functional can be computed by taking the expected value of the product of this functional and multiple white noise of the Levy process.