Asymptotic behavior of nonlinear filters

Since H. Kunita's 1971 paper "Asymptotic Behavior of the Nonlinear Filtering Errors of Markov Processes" (J. Multivariate Analysis), the subject of optimal "steady state" estimators for nonlinear diffusions has received little attention. We report on some preliminary results on this class of problems, including an examination of the asymptotic properties of solutions of the Duncan-Mortonsen-Zakai Equation.