[Équations différentielles doublement stochastiques rétrogrades réfléchies gouvernées par un processus de Lévy]
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.
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@article{CRMATH_2010__348_7-8_439_0,
author = {Ren, Yong},
title = {Reflected backward doubly stochastic differential equations driven by a {L\'evy} process},
journal = {Comptes Rendus. Math\'ematique},
pages = {439--444},
publisher = {Elsevier},
volume = {348},
number = {7-8},
year = {2010},
doi = {10.1016/j.crma.2009.11.004},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.11.004/}
}
TY - JOUR AU - Ren, Yong TI - Reflected backward doubly stochastic differential equations driven by a Lévy process JO - Comptes Rendus. Mathématique PY - 2010 SP - 439 EP - 444 VL - 348 IS - 7-8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.11.004/ DO - 10.1016/j.crma.2009.11.004 LA - en ID - CRMATH_2010__348_7-8_439_0 ER -
%0 Journal Article %A Ren, Yong %T Reflected backward doubly stochastic differential equations driven by a Lévy process %J Comptes Rendus. Mathématique %D 2010 %P 439-444 %V 348 %N 7-8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.11.004/ %R 10.1016/j.crma.2009.11.004 %G en %F CRMATH_2010__348_7-8_439_0
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://www.numdam.org/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.
