Existence of densities for jumping S.D.E.s

18 pagesInternational audienceWe consider a jumping Markov process X(t). We study the absolute continuity of the law of X(t) for t > 0. We first consider, as Bichteler-Jacod [2] and Bichteler-Gravereaux-Jacod [1], the case where the rate of jump is constant. We state some results in the spirit of those of [2, 1], with rather weaker assumptions and simpler proofs, not relying on the use of stochastic calculus of variations. We finally obtain the absolute continuity of the law of Xx t in the case where the rate of jump depends on the spatial variable, and this last result seems to be new