Random walk approximation of BSDEs with Hölder continuous terminal condition

Abstract

In this paper, we consider the random walk approximation of the solution of a Markovian BSDE whose terminal condition is a locally Hölder continuous function of the Brownian motion. We state the rate of the $L_{2}$-convergence of the approximated solution to the true one. The proof relies in part on growth and smoothness properties of the solution $u$ of the associated PDE. Here we improve existing results by showing some properties of the second derivative of $u$ in space.