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

Nicolas Fournier (1, 2) , Jean-Sébastien Giet (1)

1 IECN - Institut Élie Cartan de Nancy
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We 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.

Keywords: Stochastic differential equations; Jump processes; Absolute continuity

Domains: Probability [math.PR]

Nicolas Fournier, Jean-Sébastien Giet. Existence of densities for jumping S.D.E.s. Stochastic Processes and their Applications, 2005, 116 (4), pp.643-661. ⟨hal-00140440⟩