Asymptotic behavior of the transition density for jump type processes in small time

Abstract

The Markov process of pure jump type given by S.D.E. has a smooth density under non-degeneracy conditions both on the coefficient and on the Levy measure of the driving Levy process. In this case we obtain an estimate of this density when the time parameter is small. In this way we extend the Leandre estimate of the density for pure jump processes.