A simple formula for conditional Wiener integrals with applications

Abstract

Yen's inversion formula for conditional Wiener integrals is very complicated to apply when the conditioning function is vector-valued. This paper gives a very simple formula for such integrals. In particular, we express the conditional Wiener integral directly in terms of an ordinary (i.e., nonconditional) Wiener integral. Using this new formula, it is very easy to generalize the Kac-Feynman formula and also to obtain a Cameron-Martin type translation theorem for general conditional Wiener integrals.