A Gauss-Poisson Correspondence and the Lévy Laplacian

抄録

In this paper we present recent results on infinite dimensional Laplacians. In particular, by introducing the operator which transfers regular white noise functionals to functionals of exponential white noise, we give a relationship between an infinite dimensional Fourier-Mehler transform and the Lévy Laplacian. The operator implies a Gauss-Poisson correspondence if we consider the Lévy Laplacian acting on multiple Wiener integrals by some Lévy process. We also give an infinite dimensional random field associated with the Lévy Laplacian.