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$L^{2}$ $L^{2}$ -regularity result for solutions of backward doubly stochastic differential equations
- Achref Bachouch and
- Anis Matoussi
Stochastics and Dynamics25 Jul 2019
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We prove an $L^{2}$ $L^{2}$ -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.