Filtrage d'une diffusion reflechie a sauts, observee a travers un processus ponctuel marque

Abstract

We consider a nonlinear filtering problem, where the signal is a reflected diffusion process with jumps, and the observation is a Poisson-type marked point process, whose stochastic intensity depends on the signal. We obtain a generalized Zakai-type equation for the non-normalized conditional law by using the reference probability method. We also deduce the equation for the normalized conditional law Finally, we obtain a asymptotically efficient approximate finite dimensional filter in the special case where the signal is a continuous positive reflected diffusion in one dimension and the observation is a Poisson process with large intensity