| Título: | Smoothness of the law of some one-dimensional jumping S.D.E.s with non-constant rate of jump |
| Autores: | Fournier, Nicolas; Université Paris Est |
| Fecha: | 2008-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Stochastic differential equations, Jump processes, Regularity of the density 60H10, 60J75. |
| Descripción: | 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. |
| Idioma: | No aplica |
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