Smooth Densities for Stochastic Differential Equations with Jumps
نویسنده
چکیده
We consider a solution xt to a generic Markovian jump diffusion and show that for any t0 > 0 the law of xt0 has a C ∞ density with respect to Lebesgue measure under a uniform version of Hörmander’s conditions. Unlike previous results in the area the result covers a class of infinite activity jump processes. The result is accompolished by using carefully crafted refinements to the classical arguments used in proving the smoothness of density via Malliavin calculus. In particular, we provide a proof that the semimartinagale inequality of Norris persists for discontinuous semimartingales when the jumps are small.
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