Backward doubly stochastic differential equations with a superlinear growth generator

Abstract : Abstract We deal with backward doubly stochastic differential equations (BDSDEs) with a superlinear growth generator and a square integrable terminal datum. We introduce a new local condition on the generator, then we show that it ensures the existence and uniqueness as well as the stability of solutions. Our work goes beyond the previous results on the multidimensional BDSDEs. Although we are focused on the multidimensional case, our uniqueness result is new for one-dimensional BDSDEs, too. As an application, we establish the existence of a Sobolev solution to \SPDEs\ with superlinear growth generator. Some illustrative examples are also presented.
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https://hal-univ-tln.archives-ouvertes.fr/hal-01297351
Contributor : Khaled Bahlali <>
Submitted on : Monday, April 4, 2016 - 11:00:35 AM
Last modification on : Tuesday, June 19, 2018 - 3:50:01 PM

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Khaled Bahlali, Rafika Gatt, Badreddine Mansouri. Backward doubly stochastic differential equations with a superlinear growth generator. Comptes Rendus Mathématique, Elsevier Masson, 2015, 353, pp.25 - 30. ⟨10.1016/j.crma.2014.10.008⟩. ⟨hal-01297351⟩

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