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hal-00403667, version 1

## Numerical scheme for backward doubly stochastic differential equations

Auguste Aman () 1

This work is partially performed when the author stay at Cadi Ayyad university (2009)

Abstract: We study a discrete-time approximation for solutions of systems of decoupled forward-backward doubly stochastic differential equations (FBDSDEs). Assuming that the coefficients are Lipschitz-continuous, we prove the convergence of the scheme when the step of time discretization, $|\pi|$ goes to zero. The rate of convergence is exactly equal to $|\pi|^{1/2}$. The proof is based on a generalization of a remarkable result on the $^{2}$-regularity of the solution of the backward equation derived by J. Zhang

• 1:  Laboratoire de Mathématiques Appliquées et Informatique (LMAI)
• Université de Cocody
• Domain : Mathematics/Probability
• Keywords : Backward doubly SDEs – Discrete-time approximation
• Comment : 17 page – submitted to Electronic journal of Probability

• hal-00403667, version 1
• oai:hal.archives-ouvertes.fr:hal-00403667
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• Submitted on: Saturday, 11 July 2009 15:20:55
• Updated on: Sunday, 12 July 2009 14:04:40