Nonlinear filtering approximations by Ovcyannikov-Treves operators

Recent results in nonlinear filtering have confirmed the traditional belief that the existence of finite dimensional recursive filters for a general nonlinear system is an exception rather than a rule. It is important to know when and how one can construct finite dimensional filters that approximate certain statistics of the nonlinear system. In this paper, we present some preliminary results on constructing approximate solutions to the "pathwise" version of the Zakai equation.