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Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 1, Pages 1-17

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 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.


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).