@article{EJP480,
author = {Nicolas Fournier},
title = {Smoothness of the law of some one-dimensional jumping S.D.E.s with non-constant rate of jump},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {13},
year = {2008},
keywords = {Stochastic differential equations, Jump processes, Regularity of the density},
abstract = {We consider a one-dimensional jumping Markov process, solving a Poisson-driven stochastic differential equation. We prove that the law of this process admits a smooth density for all positive times, under some regularity and non-degeneracy assumptions on the coefficients of the S.D.E. To our knowledge, our result is the first one including the important case of a non-constant rate of jump. The main difficulty is that in such a case, the process is not smooth as a function of its initial condition. This seems to make impossible the use of Malliavin calculus techniques. To overcome this problem, we introduce a new method, in which the propagation of the smoothness of the density is obtained by analytic arguments.},
pages = {no. 6, 135-156},
issn = {1083-6489},
doi = {10.1214/EJP.v13-480},
url = {http://ejp.ejpecp.org/article/view/480}}