Comptes Rendus
no. 9
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 Bahlali1, 2 ; E.H. Essaky3 ; M. Hassani3 ; Etienne Pardoux4
1 UFR sciences, UTV, BP 132, 83957 La Garde cedex, France
2 Centre de physique théorique, CNRS Luminy, case 907, 13288 Marseille cedex 9, France
3 Université Cadi Ayyad, faculté des sciences Semlalia, département de mathématiques, BP 2390, 40000 Marrakech, Morocco
4 LATP, CNRS-UMR 6632, CMI, Université de Provence, 39, rue F. Joliot-Curie, 13453 Marseille cedex 13, France
Comptes Rendus. Mathématique, Volume 335 (2002) no. 9, pp. 757-762.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02542-6
Khaled Bahlali 1, 2 ; E.H. Essaky 3 ; M. Hassani 3 ; Etienne Pardoux 4

1 UFR sciences, UTV, BP 132, 83957 La Garde cedex, France
2 Centre de physique théorique, CNRS Luminy, case 907, 13288 Marseille cedex 9, France
3 Université Cadi Ayyad, faculté des sciences Semlalia, département de mathématiques, BP 2390, 40000 Marrakech, Morocco
4 LATP, CNRS-UMR 6632, CMI, Université de Provence, 39, rue F. Joliot-Curie, 13453 Marseille cedex 13, France 
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     title = {Existence, uniqueness and stability of backward stochastic differential equations with locally monotone coefficient},
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Khaled Bahlali; E.H. Essaky; M. Hassani; Etienne Pardoux. Existence, uniqueness and stability of backward stochastic differential equations with locally monotone coefficient. Comptes Rendus. Mathématique, Volume 335 (2002) no. 9, pp. 757-762. doi : 10.1016/S1631-073X(02)02542-6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02542-6/

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