Journal of Applied Mathematics and Stochastic Analysis
Volume 2004 (2004), Issue 2, Pages 123-136
doi:10.1155/S1048953304306027
Prevalence of backward stochastic differential equations with unique solution
1UFR Sciences, Université de Toulon et du Var, BP 132, La Garde Cedex 83957, France
2Centre de Physique Théorique, Centre National de la Recherche Scientifique, Luminy, Case 907, Marseille Cedex 9 13288, France
3Département de Mathématiques, Université Mohamed Khider, BP 145, Biskra 07000, Algeria
4Département de Mathématiques, Faculté des Sciences Semlalia, Université Cadi Ayyad, BP 2390, Marrakesh 40000, Morocco
Received 20 June 2003; Revised 15 February 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.
Abstract
We prove that in the sense of Baire category, almost all backward stochastic differential equations (BSDEs) with bounded and continuous coefficient have the properties of existence and uniqueness of solutions as well as the continuous dependence of solutions on the coefficient and the L2-convergence of their associated successive approximations.