On some finite dimensional nonlinear filters for certain diffusions observed in correlated noise (Q1076659)

This work deals with the problem of finding nonlinear filtering problems admitting finite-dimensional filters; a class of such problems was described by \textit{V. Beneš} [Stochastics 5, 65-92 (1981; Zbl 0458.60030)]: the state and observation noises were independent and the coefficients of the equations were assumed to satisfy some algebraic conditions. The goal of this work is to introduce a class where the state and observation noises are correlated; algebraic conditions on the coefficients are again derived, using the stochastic Feynman-Kač formula.