Asymptotic study of estimation in filtering for linear systems with jump parameters

In this work, we study the nonlinear filtering problem for a linear diffusion process X, the coefficients of which are fed by a Markovian jump process Z. The state process (Z,X) is assumed to be observed with additive observation noise of order /spl epsiv/. We derive approximate finite dimensional filters which are solutions of stochastic differential equations driven by the observation process; they are asymptotically efficient as /spl epsiv//spl rarr/0. Upper bounds for the corresponding errors are given.