Authors: JAE GIL CHOI

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.

Keywords: Cameron-Storvick theorem, generalized analytic Feynman integral, Gaussian process, generalized Brownian motion process, Paley-Wiener-Zygmund stochastic integral

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