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Smoothness of the law of some one-dimensional jumping S.D.E.s with non-constant rate of jump

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1.	Title	Title of document	Smoothness of the law of some one-dimensional jumping S.D.E.s with non-constant rate of jump
2.	Creator	Author's name, affiliation, country	Nicolas Fournier; Université Paris Est
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Stochastic differential equations, Jump processes, Regularity of the density
3.	Subject	Subject classification	60H10, 60J75.
4.	Description	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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2008-01-30
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/480
10.	Identifier	Digital Object Identifier	10.1214/EJP.v13-480
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 13
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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