Systems with Markovian jump parameters: Approximations for the nonlinear filtering problem

The filtering problem of systems with Markovian jump parameters is considered. Since computing the optimal solution of such problems remains most often untractable. approximate solutions are usually sought. Here we present such an approximation, but defined in a rigourous sense by extending some previous results obtained by Di Masi and Runggaldier [Di 81] on diffusion processes.