A criterion for filtering in semimartingale models

Recently there has been a growing interest in the problems of inference for stochastic processes when the underlying distribution is not specified in terms of a parametric family. Godambe's (1985) approach is here employed to obtain estimates for random signals for a continuous semimartingale model. The method, which avoids specification of the underlying distribution, leads to estimation for nonconjugate prior situations which is computationally attractive as well as optimal in a restricted sense. A number of techniques in the recent literature are special cases.