Smoothness properties of the conditional expectation in finitely additive white noise filtering

AbstractIt is shown that for a wide class of signal processes and bounded g, the conditional expectation π(g, y) in the white noise filtering model is a C∞-functional of the observations in the sense that π(g, y) and its Fréchet derivatives (which exist) are random variables on the quasicylindrical probability space on which the observation model is defined