Inversion of conditional Wiener integrals

Abstract

Summary:In this paper, we introduce a simple formula for conditional Wiener integrals over $C_0(mathbb{B})$, the space of abstract Wiener space valued continuous functions. Using this formula, we establish various formulas for a conditional Wiener integral and a conditional Feynman integral of functionals on $C_0(mathbb{B})$ in certain classes which correspond to the classes of functionals on the classical Wiener space introduced by Cameron and Storvick. We also evaluate the conditional Wiener integral and conditional Feynman integral for functionals of the form [ exp iggl lbrace int _0^T heta (s, x(s))mathrm{d}eta (s) iggr brace ] which are of interest in Feynman integration theories and quantum mechanics