Turkish Journal of Mathematics
DOI
10.3906/mat-2104-90
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
First Page
2746
Last Page
2758
Recommended Citation
CHOI, JAE GIL
(2021)
"Cameron-Storvick theorem associated with Gaussian paths on function space,"
Turkish Journal of Mathematics: Vol. 45:
No.
6, Article 24.
https://doi.org/10.3906/mat-2104-90
Available at:
https://journals.tubitak.gov.tr/math/vol45/iss6/24
