Probability Theory
A generalized existence theorem of BSDEs
Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 685-688.

In this Note, we deal with one-dimensional backward stochastic differential equations (BSDEs) where the coefficient is left-Lipschitz in y (may be discontinuous) and Lipschitz in z, but without explicit growth constraint. We prove, in this setting, an existence theorem for backward stochastic differential equations.

Dans cette Note, nous traitons l'équation différentielle stochastique rétrograde en une dimension, où le coéfficient est Lipschitzien à gauche en y (peut-être discontinu) et Lipschitzien en z, sans croissance contrainte explicite. Nous montrons, dans ce cas, un théorème d'existence de la solution pour équation différentielle stochastique rétrograde.

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DOI: 10.1016/j.crma.2006.02.020
Jia, Guangyan 1

1 School of Mathematics and System Sciences, Shandong University, Jinan, Shandong, 250100, P.R. China
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Jia, Guangyan. A generalized existence theorem of BSDEs. Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 685-688. doi : 10.1016/j.crma.2006.02.020. http://www.numdam.org/articles/10.1016/j.crma.2006.02.020/

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