[Existence, unicité et stabilité des équations différentielles stochastiques rétrogrades à coefficient localement monotone]
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.
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@article{CRMATH_2002__335_9_757_0,
author = {Bahlali, Khaled and Essaky, E.H. and Hassani, M. and Pardoux, Etienne},
title = {Existence, uniqueness and stability of backward stochastic differential equations with locally monotone coefficient},
journal = {Comptes Rendus. Math\'ematique},
pages = {757--762},
publisher = {Elsevier},
volume = {335},
number = {9},
year = {2002},
doi = {10.1016/S1631-073X(02)02542-6},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02542-6/}
}
TY - JOUR AU - Bahlali, Khaled AU - Essaky, E.H. AU - Hassani, M. AU - Pardoux, Etienne TI - Existence, uniqueness and stability of backward stochastic differential equations with locally monotone coefficient JO - Comptes Rendus. Mathématique PY - 2002 SP - 757 EP - 762 VL - 335 IS - 9 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02542-6/ DO - 10.1016/S1631-073X(02)02542-6 LA - en ID - CRMATH_2002__335_9_757_0 ER -
%0 Journal Article %A Bahlali, Khaled %A Essaky, E.H. %A Hassani, M. %A Pardoux, Etienne %T Existence, uniqueness and stability of backward stochastic differential equations with locally monotone coefficient %J Comptes Rendus. Mathématique %D 2002 %P 757-762 %V 335 %N 9 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(02)02542-6/ %R 10.1016/S1631-073X(02)02542-6 %G en %F CRMATH_2002__335_9_757_0
Bahlali, Khaled; Essaky, E.H.; Hassani, M.; Pardoux, Etienne. Existence, uniqueness and stability of backward stochastic differential equations with locally monotone coefficient. Comptes Rendus. Mathématique, Tome 335 (2002) no. 9, pp. 757-762. doi : 10.1016/S1631-073X(02)02542-6. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02542-6/
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