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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
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
© 2015 by De Gruyter