Let xtbe a diffusion process satisfying a stochastic differential equation of the formwhere [Wtilde] is an n-dimensional Brownian motion. Let the observed process ytbe related to xtby,where W is one dimensional Brownian motion Independent of [Wtilde]. The measure γ is a random counting measure independent of [Wtilde] and W. The problem is to find the conditional probability of the process xtgiven the observed path yt0. The results of absolute continuity of measures are used to derive a stochastic differential equation for the required conditional probability .Our results are easily extended to the case where the process xtis governed by a stochastic differential equation also containing jump process, as indicated in Remark 1. Our results also cover the filter equation given by Gertner [4], Di Masi [5] and Pardoux [6] . Further, Zakaitype equation (linear stochastic partial differential equation) corresponding to the systems considered by Shiryayev [3] and Snyder [9], which are of Kushner type (nonlinear stochastic partial differential equation), also follow from our main results . Finally, some open questions arising from this work are discussed in Remark 2