On the existence of smooth densities for jump processes
成果类型：
Article
署名作者：
Picard, J
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
发表日期：
1996
页码：
481-511
关键词：
摘要：
We consider a Levy process X(t) and the solution Y-t of a stochastic differential equation driven by X(t); we suppose that X(t) has infinitely many small jumps, but its Levy measure may be very singular (for instance it may have a countable support). We obtain sufficient conditions ensuring the existence of a smooth density for Y-t: these conditions are similar to those of the classical Malliavin calculus for continuous diffusions. More generally, we study the smoothness of the law of variables F defined on a Poisson probability space; the basic tool is a duality formula from which we estimate the characteristic function of F.