Geodesic
Probability Theory
Reflected backward doubly stochastic differential equations driven by a Lévy process
[Équations différentielles doublement stochastiques rétrogrades réfléchies gouvernées par un processus de Lévy]

Présenté par : Marc Yor

Ren, Yong1
1 Department of Mathematics, Anhui Normal University, Wuhu 241000, China
Comptes Rendus. Mathématique, Tome 348 (2010) no. 7-8, pp. 439-444.

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We prove the existence and uniqueness of a solution for reflected backward doubly stochastic differential equations (RBDSDEs) driven by Teugels martingales associated with a Lévy process, in which the obstacle process is right continuous with left limits (càdlàg), via Snell envelope and the fixed point theorem.

On démontre l'existence et l'unicité de la solution d'équations différentielles doublement stochastiques rétrogrades réfléchies (RBDSDE) gouvernées par des martingales de Teugels associées à un processus de Lévy dans lequel le processus obstacle est continu à droite et possède une limite à gauche (càdlàg), via l'enveloppe de Snell et un théorème de point fixe.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.11.004

Ren, Yong 1

1 Department of Mathematics, Anhui Normal University, Wuhu 241000, China 
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Ren, Yong. Reflected backward doubly stochastic differential equations driven by a Lévy process. Comptes Rendus. Mathématique, Tome 348 (2010) no. 7-8, pp. 439-444. doi : 10.1016/j.crma.2009.11.004. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2009.11.004/

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☆ The work is supported by the National Natural Science Foundation of China (Project 10901003) and the Great Research Project of Natural Science Foundation of Anhui Provincial Universities.