A filtering problem with a small nonlinear term

In this paper, we consider a filtering problem where the signal X _t satisfies a slightly nonlinear stochastic differential equation and we want to obtain estimates of X _t. To this end, we decompose the nonlinearity with two techniques—a deterministic one and a stochastic one—and this leads us to two sequences of estimates which can be computed by solving finite dimensional equations. We want to compare their performances: we solve this problem in most cases if we restrict ourselves to sufficiently small times t and we give conditions which permit to conclude also for larger times