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 $dP_w/dP_y$.
Citation
Thomas Kailath. Moshe Zakai. "Absolute Continuity and Radon-Nikodym Derivatives for Certain Measures Relative to Wiener Measure." Ann. Math. Statist. 42 (1) 130 - 140, February, 1971. https://doi.org/10.1214/aoms/1177693500
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