Polynomial approximation for a class of physical random variables

Abstract

In white noise theory on Hilbert spaces, it is known that maps which are uniformly continuous around the origin in the S-topology constitute an important class of "physical" random variables. We prove that random variables having such a continuity property can be approximated in the gaussian measure by polynomial random variables. The proof relies on representing functions which are uniformly S-continuous around the origin as the composition of a continuous map with a Hilbert-Schmidt operator.