Bulletin of the
Korean Mathematical Society BKMS

In this paper, we first develop a general formula for evaluating conditional abstract Wiener integrals of cylinder functions. We next use our formula to evaluate the conditional abstract Wiener integral of various cylinder functions and then specialize our results to conditional Yeh-Wiener integrals to show that we can obtain the corresponding results by Park and Skoug. We finally obtain a Cameron-Martin translation theorem for conditional abstract Wiener integrals.

Keywords: abstract Wiener space, conditional abstract Wiener integral, Yeh-Wiener space, conditional Yeh-Wiener integral, Cameron-Martin translation theorem

MSC numbers: Primary 28C20