The integration by parts formula in the Meixner white noise analysis

Abstract

Using a general approach that covers the cases of Gaussian, Poissonian, Gamma, Pascal and Meixner measures on an infinite- dimensional space, we construct a general integration by parts formula for analysis connected with each of these measures. Our consideration is based on the constructions of the extended stochastic integral and the stochastic derivative that are connected with the structure of the extended Fock space.