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Journal of Applied Mathematics and Stochastic Analysis
Volume 2004, Issue 4, Pages 317-335
http://dx.doi.org/10.1155/S1048953304310038

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 Hindawi Publishing Corporation. 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.

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.