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Comptes Rendus Mathématique
Volume 335, n° 9
pages 757-762 (novembre 2002)
Doi : S1631-073X(02)02542-6
Received : 4 June 2002 ;  accepted : 26 July 2002
Existence, uniqueness and stability of backward stochastic differential equations with locally monotone coefficient
Existence, unicité et stabilité des équations différentielles stochastiques rétrogrades à coefficient localement monotone

Khaled Bahlali a, b, 1 , E.H Essaky c, 2 , M Hassani c, 3 , Etienne Pardoux d
a UFR sciences, UTV, BP 132, 83957 La Garde cedex, France 
b Centre de physique théorique, CNRS Luminy, case 907, 13288 Marseille cedex 9, France 
c Université Cadi Ayyad, faculté des sciences Semlalia, département de mathématiques, BP 2390, 40000 Marrakech, Morocco 
d LATP, CNRS-UMR 6632, CMI, Université de Provence, 39, rue F. Joliot-Curie, 13453 Marseille cedex 13, France 

Note presented by Paul Malliavin


We prove existence, uniqueness and stability of the solution for multidimensional backward stochastic differential equations (BSDE) with locally monotone coefficient. This is done with an almost quadratic growth coefficient and a square integrable terminal data. The coefficient could be neither locally Lipschitz in the variable y nor in the variable z . To cite this article: K. Bahlali et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 757-762.

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Nous prouvons l'existence, l'unicité et la stabilité des solutions d'équations différentielles stochastiques rétrogrades (EDSR), dont le coefficient vérifie une condition de type monotonie locale. Ces resultats sont obtenus avec un coefficient de croissance presque quadratique et une donnée terminale de carré intégrable. De plus le coefficient peut être ni localement Lipschitz en y ni en z . Pour citer cet article : K. Bahlali et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 757-762.

The full text of this article is available in PDF format.
1  Partially supported by CNRS/DEF, PICS, 2002.
2  Partially supported by convention CNCPRST Maroc/CNRS France, projet 8310 2001.
3  Supported by CMIFM, A.I. n MA/01/02.

© 2002  Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. All Rights Reserved.
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