Anticipated BDSDEs driven by Lévy process with non-Lipschitz coefficients

Sadibou Aidara; Ahmadou Bamba Sow

doi:10.1515/rose-2014-0040

Published by De Gruyter August 25, 2015

Anticipated BDSDEs driven by Lévy process with non-Lipschitz coefficients

Sadibou Aidara and Ahmadou Bamba Sow

From the journal Random Operators and Stochastic Equations

https://doi.org/10.1515/rose-2014-0040

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Abstract

In this work we deal with a anticipated backward doubly stochastic differential equation associated to a random Poisson measure. We establish existence and uniqueness of solution in the case of non-Lipschitz coefficients. The novelty of our result lies in the fact that we allow the time interval to be infinite.

Keywords: Anticipated backward doubly stochastic differential equation; random Poisson measure; Itô's representation formula; Gronwall lemma

MSC: 60H05; 60G44

Funding source: African Center of Excellence

Award Identifier / Grant number: CEA-MITIC

Funding source: Faculty of Applied Sciences and Technology at Université Gaston Berger de Saint-Louis

Award Identifier / Grant number: World Bank program

Received: 2015-4-29

Accepted: 2015-7-3

Published Online: 2015-8-25

Published in Print: 2015-9-1