Numerical scheme for backward doubly stochastic differential equations

Details Numerical scheme for backward doubly stochastic differential equations Numerical scheme for backward doubly stochastic differential equations

2009-07-12

arxiv.org/abs/0907.2035v1

Mathematics

Probability

17 page; submitted to Electronic journal of Probability

Scientific paper

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

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