The finitely additive nonlinear filtering problem for the model yt = ht(Xt)+et is solved when the function h is unbounded and satisfies no growth conditions whatever.

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...

In the nonlinear filtering model with signal and observation noise independent, we show that the filter depends continuously on the law of the signal. We do not assume that the signal process is Markov and prove the result under minimal integrability conditions. The analysis is based on...

A concept of divisibility is introduced for stochastic difference equations. Infinite divisibility then leads to a continuous time process in which a nested sequence of divisible stochastic difference equations can be embedded.

In this paper we formulate and prove a general principle which enables us to deduce limit theorems for a sequence of random variables on a finitely additive probability space.

We consider the question of robustness of the optimal nonlinear filter when the signal process X and the observation noise are possibly correlated. The signal X and observations Y are given by a SDE where the coefficients can depend on the entire past. Using results on pathwise solutions of...