Filtrage d'un système càd-làg:application du calcul des variations stochastiques à l'existence d'une densiteé

Abstract

This work is devoted to deriving the density of the filter in a filtering problem with cad-lag signal and observation. The signal and observation processes satisfy some stochastic differential equations with jumps where the intensity measures of jumps depend on the signal process. The Kushner-Stratonovitch and Zakai equations are established using the method of the reference probability. The main tool to show the absolute continuity of the filter is the stochastic calculus of variations. A sufficient condition on the coefficients of the SDE's governing the signal and the observation, to ensure the existence of the density of the filter, is given