Conditional generalized analytic Feynman integrals and a generalized integral equation (Q1578980)

\textit{R. H. Cameron} and \textit{D. A. Storvick} [Lect. Notes Math. 798, 18-67 (1980; Zbl 0439.28007)] introduced a Banach algebra \(S(L^2[0, T])\) of functionals on a Wiener space, which are a kind of stochastic Fourier transform of complex Borel measures on \(L^2[0, T]\). Then they proved the existence of the analytic Feynman integral for functionals in \(S(L^2[0, T])\). \textit{D. M. Chung} and \textit{D. Skoug} [SIAM J. Math. Anal. 20, No. 4, 950-965 (1989; Zbl 0678.28007)] introduced the concept of a conditional Feynman integral of a functional on a Wiener space and established the existence of the conditional analytic Feynman integral for all functionals in \(S(L^2[0, T])\). In the present paper, the results concerning Feynman integrals are extended to those of functionals involving a more general stochastic process. This is a process subject to drift and it is nonstationary in time. This conditional generalized analytic Feynman integral is used to provide a solution to an integral equation formally equivalent to the generalized Schrödinger equation.