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

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