Reflected backward doubly stochastic differential equations driven by a Lévy process

Yong Ren

doi:10.1016/j.crma.2009.11.004

Probability Theory

Reflected backward doubly stochastic differential equations driven by a Lévy process

Presented by: Marc Yor

Yong Ren ¹

¹ Department of Mathematics, Anhui Normal University, Wuhu 241000, China

Comptes Rendus. Mathématique, Volume 348 (2010) no. 7-8, pp. 439-444.

Abstract
Résumé

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.

Received: 2009-09-24
Accepted: 2009-11-05
Published online: 2010-03-12

DOI: 10.1016/j.crma.2009.11.004

Author's affiliations:

Yong Ren ¹

¹ Department of Mathematics, Anhui Normal University, Wuhu 241000, China

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     title = {Reflected backward doubly stochastic differential equations driven by a {L\'evy} process},
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     doi = {10.1016/j.crma.2009.11.004},
     language = {en},
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Yong Ren. Reflected backward doubly stochastic differential equations driven by a Lévy process. Comptes Rendus. Mathématique, Volume 348 (2010) no. 7-8, pp. 439-444. doi : 10.1016/j.crma.2009.11.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.11.004/

References
Cited by

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[7] Y. Ren; L. Hu Reflected backward stochastic differential equation driven by Lévy processes, Statist. Probab. Lett., Volume 77 (2007), pp. 1559-1566

[8] Y. Ren; A. Lin; L. Hu Stochastic PDIEs and backward doubly stochastic differential equations driven by Lévy processes, J. Comput. Appl. Math., Volume 223 (2009), pp. 901-907

Cited by Sources:

^☆ 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.

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