Comptes Rendus
no. 7-8
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

Yong Ren1
1 Department of Mathematics, Anhui Normal University, Wuhu 241000, China
Comptes Rendus. Mathématique, Volume 348 (2010) no. 7-8, pp. 439-444.

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.

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.

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

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[2] S. Hamadène Reflected BSDEs with discontinuous barrier and applications, Stochastics Stochastics Rep., Volume 74 (2002), pp. 571-596

[3] S. Hamadène; Y. Ouknine Reflected backward stochastic differential equations with jumps and random obstacle, Electron. J. Probab., Volume 8 (2003), pp. 1-20

[4] S. He; J. Wang; J. Yan Semimartingale and Stochastic Analysis, Scientific Press, Beijing, 1995

[5] J.-P. Lepeltier; M. Xu Penalization method for reflected backward stochastic differential equations with one r.c.l.l. barrier, Statist. Probab. Lett., Volume 75 (2005), pp. 58-66

[6] D. Nualart; W. Schoutens Chaotic and predictable representation for Lévy processes, Stochastic Process. Appl., Volume 90 (2000), pp. 109-122

[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

Cité par 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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