Nonlinear filtering: Interacting particle resolution

In this Note, we study interacting particle approximations of discrete time and measure valued dynamical systems. Such systems have arisen in such diverse Scientific disciplines as in Propagation of Chaos Theory (see [12] and [19]), and in Nonlinear Filtering Theory. The main contribution of this Note is to prove the convergences to the optimal filter of such approximations, yielding what seemed to be the first mathematically well-founded convergence results for such approximations of the nonlinear filtering equations. This new treatment was influenced primarily by the development of genetic algorithms (see [16] and [3]), and secondarily by the papers of H. Kunita and L. Stettner, [17] and [18] respectively.