Journal of Applied Mathematics and Stochastic Analysis 
Volume 2004 (2004), Issue 4, Pages 317-335
doi:10.1155/S1048953304310038

Backward stochastic differential equations with stochastic monotone coefficients

K. Bahlali,1 A. Elouaflin,2 and M. N'zi2

 1UFR des Sciences, Universitéde Toulon-Var (UTV), BP 132, La Garde Cedex 83957, France
2UFR de Mathématiques et Informatique, Université de Cocody, Abidjan 22 BP 582, Cote D'Ivoire
Received 25 October 2003; Revised 24 June 2004

Abstract

We prove an existence and uniqueness result for backward stochastic differential equations whose coefficients satisfy a stochastic monotonicity condition. In this setting, we deal with both constant and random terminal times. In the random case, the terminal time is allowed to take infinite values. But in a Markovian framework, that is coupled with a forward SDE, our result provides a probabilistic interpretation of solutions to nonlinear PDEs.