Abstract
We consider a Markovian jump process θ, with finite state space, feeding the parameters of a nonlinear diffusion process X. We observe θ and X in white noise, and—given a function f—we want to construct a finite filter for the f(X t )-process. An algorithm is investigated which will produce a finite filter if it halts after a finite number of steps, and we give necessary and. sufficient conditions for this to happen.