Integration-by-Parts Characterizations of Gaussian Processes

Abstract

The Malliavin integration-by-parts formula is a key ingredient to develop stochastic analysis on the Wiener space. In this article we show that a suitable integration-by-parts formula also characterizes a wide class of Gaussian processes, the so-called Gaussian Fredholm processes.

Keywords: Gaussian processes, Malliavin calculus, Stein's lemma