Absolute Continuity and Radon-Nikodym Derivatives for Certain Measures Relative to Wiener Measure

Abstract

We give sufficient conditions for the absolute continuity relative to Wiener measure, $P_w$, of a measure, $P_y$, induced by the sum, $y(t)$, of a Wiener process and a non-anticipating and differentiable "signal" process. When the signal process is a measurable function of $y$, we also give expressions for $dP_y/dP_w$ and $dP_w/dP_y$.