Stochastic and Multiple Wiener Integrals for Gaussian Processes

Abstract

Multiple Wiener integrals and stochastic integrals are defined for Gaussian processes, extending the related notions for the Wiener process. It is shown that every $L_2$-functional of a Gaussian process admits an adapted stochastic integral representation and an orthogonal series expansion in terms of multiple Wiener integrals. Also some results of Wiener's theory of nonlinear noise are generalized to noises other than white.