Turkish Journal of Mathematics
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.
DOI
10.3906/mat-2104-90
Keywords
Cameron-Storvick theorem, generalized analytic Feynman integral, Gaussian process, generalized Brownian motion process, Paley-Wiener-Zygmund stochastic integral
First Page
2746
Last Page
2758
Recommended Citation
CHOI, J. G (2021). Cameron-Storvick theorem associated with Gaussian paths on function space. Turkish Journal of Mathematics 45 (6): 2746-2758. https://doi.org/10.3906/mat-2104-90
