Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 1, Pages 1-17
doi:10.1155/S1048953303000017
BSDE associated with Lévy processes and application to PDIE
1UFR Sciences, UVT, BP 132, La Garde Cedex 83957, France
2CPT, CNRS, Luminy. Case 907, Marseille Cedex 9 13288, France
3Université Cadi Ayyad, Faculté des Sciences et Techniques, Départment de Math & Info., Marrakech BP 549, Morocco
4Université Cadi Ayyad, Faculté des Sciences Semlalia, Département de Mathématiques, Marrakech BP 2390, Morocco
Received 1 April 2002; Revised 1 November 2002
Copyright © 2003 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 deal with backward stochastic differential equations (BSDE for short) driven by
Teugel's martingales and an independent Brownian motion. We study the existence,
uniqueness and comparison of solutions for these equations under a Lipschitz as well as
a locally Lipschitz conditions on the coefficient. In the locally Lipschitz case, we prove
that if the Lipschitz constant LN behaves as log(N) in the ball B(0,N), then the corresponding BSDE has a unique solution which depends continuously on the on the coefficient and the terminal data. This is done with an unbounded terminal data. As application, we give a probabilistic interpretation for a large class of partial differential
integral equations (PDIE for short).