Numerical scheme for backward doubly stochastic differential equations

2009/07/12 by Aman, Auguste
#60H07 #62G08 #65C05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.0907.2035

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, |π| goes to zero. The rate of convergence is exactly equal to |π|^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

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