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$L^{2}$ -regularity result for solutions of backward doubly stochastic differential equations

Achref Bachouch

Matematisk Institutt, Universitetet i Oslo, Postboks 1053 Blindern, 0316 Oslo, Norway

E-mail Address: achref.bachouch@gmail.com

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and

Anis Matoussi

Institut du Risque et de l’Assurance, LMM, FR. CNRS N. 2962, Avenue Messiaen, 72089 Le Mans, France

E-mail Address: anis.matoussi@univ-lemans.fr

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https://doi.org/10.1142/S0219493720500124Cited by:1 (Source: Crossref)

Abstract

We prove an $L^{2}$ -regularity result for the solutions of Forward Backward doubly stochastic differential equations (F-BDSDEs) under globally Lipschitz continuous assumptions on the coefficients. As an application of our result, we derive the rate of convergence in time for the (Euler time discretization-based) numerical scheme for F-BDSDEs proposed by Bachouch et al. (2016) under only globally Lipschitz continuous assumptions.

Keywords:

AMSC: 60H10, 65C30

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