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Comptes Rendus Mathématique
Volume 347, n° 19-20
pages 1201-1206 (octobre 2009)
Doi : 10.1016/j.crma.2009.08.001
Received : 28 September 2008 ;  accepted : 6 August 2009
One barrier reflected backward doubly stochastic differential equations with continuous generator
Équations différentielles doublement stochastiques rétrogrades réfléchies à une barrière
 

Kahled Bahlali a, 1 , M. Hassani b, 2 , B. Mansouri c, 3 , N. Mrhardy b, 2
a IMATH, UFR Sciences, USTV, B.P. 132, 83957 La Garde cedex, France 
b Université Cadi-Ayyad, département de mathématiques et d’informatique, B.P. 4162, Safi, Morocco 
c Université Mohamed-Khider, département de mathématiques, B.P. 145, Biskra, Algeria 

Abstract

We prove the existence and uniqueness of solutions to Reflected Backward Doubly Stochastic Differential Equations (RBDSDEs) with one continuous barrier and uniformly Lipschitz coefficients. The existence of a maximal and a minimal solution for RBDSDEs with continuous generator is also established. To cite this article: K. Bahlali et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).

The full text of this article is available in PDF format.
Résumé

Nous établissons l’existence et l’unicité des solutions pour des équations différentielles doublement stochastiques rétrogrades réfléchies (EDDSRR) avec une barrière continue et des coefficients uniformement lipschitziens. Nous montrons également l’existence d’une solution maximale et d’une solution minimale pour des EDDSRR ayant un générateur continu. Pour citer cet article : K. Bahlali et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).

The full text of this article is available in PDF format.
1  Partially supported by Marie Curie ITN, No. 213841-2.
2  Partially supported by PHC Volubilis MA/142/06.
3  Partially supported by PHC Tassili 07MDU705.


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