A Transfer Principle from Wiener to Poisson Space and Applications

Abstract

The aim of this work is to construct the stochastic calculus of variations on Poisson space and some of its applications via the stochastic analysis on Wiener space. We define a new gradient operator on Wiener space, whose adjoint extends the Poisson stochastic integral. This yields a new decomposition of the Ornstein-Uhlenbeck operator and a substructure of the standard Dirichlet structure on Wiener space, with applications to stochastic analysis on Poisson space and infinite-dimensional analysis for the exponential density.