Cameron-Storvick theorem associated with Gaussian paths on function space

TL;DR

This paper extends the Cameron-Storvick theorem to a broader class of Gaussian processes on general Wiener spaces, enabling new evaluations of generalized Feynman integrals for functionals of these processes.

Contribution

It provides a more general Cameron-Storvick theorem applicable to Gaussian processes on broad Wiener spaces, enhancing integral evaluation techniques.

Findings

Extended Cameron-Storvick theorem for generalized Gaussian processes.

Derived explicit formulas for Feynman integrals of monomials.

Applied the theorem to evaluate specific stochastic integrals.

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 $\mathcal Z_k$ on a very general Wiener space $C_{a,b}[0,T]$. The general Wiener space $C_{a,b}[0,T]$ 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.