Asymptotic analysis of a class of nonlinear filtering problems - Part I: A generic example

A class of nonlinear estimation problems are considered for systems involving Markov processes. The systems are parameterized by ϵ ! 0 so that their solutions are asymptotic (weakly) to diffusion processes. When the latter are Gauss - Markov processes to which the Kalrnan-Bucy filtering algorithm applies, we compute formal power series (in ϵ) for the conditional densities in terms of the conditional density in the Kaiman-Bucy problem. A generic example is treated in detail in Part I. More general problems are outlined in Part II.