Stability of BSDEs w.r.t. Brownian motion

In this paper, we study the stability of backward stochastic diierential equations (BSDEs for short) w.r.t. the Brownian motion; more precisely, we will show that if W n is a martingale approximation of a Brownian motion W then the solution to the BSDE driven by the mar-tingale W n converges to the solution of the classical BSDE, namely the BSDE driven by W. The particular case of the scaled random walks has been studied in 2]. Here, we deal with a more general situation and we will not assume that the W n has the predictable representation property: this yields an orthogonal martingale in the BSDE driven by W n. As a byproduct of our result, we obtain the convergence of the \Euler's scheme" for BSDEs corresponding to the case where W n is a time discretization of W.