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
[Équations différentielles doublement stochastiques rétrogrades réfléchies gouvernées par un processus de Lévy]

Présenté par : 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.

Résumé
Abstract

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 : 2009-09-24
Accepté le : 2009-11-05
Publié le : 2010-03-12

DOI : 10.1016/j.crma.2009.11.004

Affiliations des auteurs :

Yong Ren ¹

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

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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/

Bibliographie
Cité par

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Djibril Ndiaye; Yaya Sagna Averaging principle for RBDSDEs with Poisson jumps, Random Operators and Stochastic Equations, Volume 33 (2025) no. 1, p. 75 | DOI:10.1515/rose-2025-2002
Mohamed Marzougue Penalization method for reflected BDSDEs with two-sided jumps and driven by Lévy process, Bulletin des Sciences Mathématiques, Volume 186 (2023), p. 103282 | DOI:10.1016/j.bulsci.2023.103282
Badr-eddine Berrhazi; Mohamed El Fatini; Astrid Hilbert; Naoual Mrhardy; Roger Pettersson RBDSDEs with jumps and optional Barrier and mean field game with common noise, Stochastics, Volume 95 (2023) no. 4, p. 615 | DOI:10.1080/17442508.2022.2113080
Mohamed Marzougue Two-barriers reflected backward doubly SDEs beyond right continuity, Random Operators and Stochastic Equations, Volume 30 (2022) no. 4, p. 271 | DOI:10.1515/rose-2022-2089
Badr-eddine Berrhazi; Mohamed El Fatini; Astrid Hilbert; Naoual Mrhardy; Roger Pettersson Reflected backward doubly stochastic differential equations with discontinuous barrier, Stochastics, Volume 92 (2020) no. 7, p. 1100 | DOI:10.1080/17442508.2019.1691207
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Yong-Kui Chang; Zhuan-Xia Cheng; G. M. N’Guérékata Stepanov-Like Pseudo Almost Automorphic Solutions to Some Stochastic Differential Equations, Bulletin of the Malaysian Mathematical Sciences Society, Volume 39 (2016) no. 1, p. 181 | DOI:10.1007/s40840-015-0168-3
Yong-Kui Chang; Chao Tang Asymptotically almost automorphic solutions to stochastic differential equations driven by a Lévy process, Stochastics, Volume 88 (2016) no. 7, p. 980 | DOI:10.1080/17442508.2016.1178748
Lanying Hu Reflected backward doubly stochastic differential equations driven by a Lévy process with stochastic Lipschitz condition, Applied Mathematics and Computation, Volume 219 (2012) no. 3, p. 1153 | DOI:10.1016/j.amc.2012.07.023
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Miguel Martínez; Jaime San Martín; Soledad Torres Numerical Method for Reflected Backward Stochastic Differential Equations, Stochastic Analysis and Applications, Volume 29 (2011) no. 6, p. 1008 | DOI:10.1080/07362994.2011.610162

Cité par 12 documents. Sources : Crossref

^☆ 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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