Journal of Applied Mathematics and Stochastic Analysis
Volume 2004 (2004), Issue 4, Pages 317-335
Backward stochastic differential equations with stochastic monotone coefficients
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
Copyright © 2004 K. Bahlali et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.