Reflected generalized backward doubly SDEs driven by Lévy processes and Applications

Auguste Aman (1)

1 LMAI - Laboratoire de Mathématiques Appliquées et Informatique

In this paper, a class of reflected generalized backward doubly stochastic differential equations (reflected GBDSDEs in short) driven by Teugels martingales associated with L\'{e}vy process and the integral with respect to an adapted continuous increasing process is investigated. We obtain the existence and uniqueness of solutions to these equations. A probabilistic interpretation for solutions to a class of reflected stochastic partial differential integral equations (PDIEs in short) with a nonlinear Neumann boundary condition is given.

Mots clés: Neumann boundary condition.; Reflected backward doubly SDEs; stochastic partial differential integral equation; Lévy process; Teugels martingale; Neumann boundary condition

Domaines: Probabilités [math.PR]

Auguste Aman. Reflected generalized backward doubly SDEs driven by Lévy processes and Applications. 2009. ⟨hal-00403669⟩