Parts formulas involving the Fourier-Feynman transform associated with Gaussian process on Wiener space
In this paper, using a very general Cameron--Storvick theorem on the Wiener space $C_0[0,T]$, we establish various integration by parts formulas involving generalized analytic Feynman integrals, generalized analytic Fourier--Feynman transforms, and the first variation (associated with Gaussian processes) of functionals $F$ on $C_0[0,T]$ having the form $F(x)=f(\langle{α_1,x}\rangle, \ldots, \langle{α_n,x}\rangle)$ for scale almost every $x\in C_0[0,T]$, where $\langle{α,x}\rangle$ denotes the Paley--Wiener--Zygmund stochastic integral $\int_0^T α(t)dx(t)$, and $\{α_1,\ldots,α_n\}$ is an orthogonal set of nonzero functions in $L_2[0,T]$. The Gaussian processes used in this paper are not stationary.
math.FA↗