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In this paper we present a weak approximation scheme for BSDEs driven by aWiener process and an (in)finite activity Poisson random measure with driversthat are general Lipschitz functionals of the solution of the BSDE. Theapproximating backward stochastic difference equations (BS\Delta Es) are drivenby random walks that weakly approximate the given Wiener process and Poissonrandom measure. We establish the weak convergence to the solution of the BSDEand the numerical stability of the sequence of solutions of the BS\Delta Es. Byway of illustration we analyse explicitly a scheme with discrete step-sizedistributions.

Convergence of BS\Delta Es driven by random walks to BSDEs: the case of (in)finite activity jumps with general driver