Cameron–Storvick theorem associated with Gaussian paths on function space

Abstract

The purpose of this paper is to provide a more general Cameron–Storvick theorem for the generalized analytic Feynman integral associated with Gaussian process Zk on a very general Wiener space Ca,b[0, T] . The general Wiener space Ca,b[0, T] can be considered as the set of all continuous sample paths of the generalized Brownian motion process determined by continuous functions a(t) and b(t) on [0, T] . As an interesting application, we apply this theorem to evaluate the generalized analytic Feynman integral of certain monomials in terms of Paley–Wiener–Zygmund stochastic integrals.