Nonlinear SDEs driven by Lévy processes and related PDEs
| dc.creator | Jourdain, Benjamin | |
| dc.creator | Méléard, Sylvie | |
| dc.creator | Woyczynski, Wojbor | |
| dc.date | 2007-07-18 | |
| dc.date.accessioned | 2026-07-07T08:19:02Z | |
| dc.date.available | 2026-07-07T08:19:02Z | |
| dc.description | In this paper we study general nonlinear stochastic differential equations, where the usual Brownian motion is replaced by a Lévy process. We also suppose that the coefficient multiplying the increments of this process is merely Lipschitz continuous and not necessarily linear in the time-marginals of the solution as is the case in the classical McKean-Vlasov model. We first study existence, uniqueness and particle approximations for these stochastic differential equations. When the driving process is a pure jump Lévy process with a smooth but unbounded Lévy measure, we develop a stochastic calculus of variations to prove that the time-marginals of the solutions are absolutely continuous with respect to the Lebesgue measure. In the case of a symmetric stable driving process, we deduce the existence of a function solution to a nonlinear integro-differential equation involving the fractional Laplacian. | |
| dc.identifier | https://arxiv.org/abs/0707.2723 | |
| dc.identifier | http://arxiv.org/abs/0707.2723 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134636 | |
| dc.subject | Probability | |
| dc.subject | 60K35, 35S10, 65C35 | |
| dc.title | Nonlinear SDEs driven by Lévy processes and related PDEs | |
| dc.type | text |