GRID-VALUED CONDITIONAL YEH-WIENER INTEGRALS AND A KAC-FEYNMAN WIENER INTEGRAL EQUATION

CHULL PARK AND DAVID SKOUG

Abstract:

In this paper we establish several results involving grid-valued conditional Yeh-Wiener integrals of the type

We develop a formula for converting these grid-valued conditional Yeh-Wiener integrals into ordinary Yeh-Wiener integrals. We also obtain a Cameron-Martin translation theorem for these integrals. More importantly, we evaluate these conditional expectations for functionals F of the form

by solving a Kac-Feynman type Wiener integral equation.