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Random walk approximation of BSDEs with H{\"o}lder continuous terminal condition
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In this paper we consider the random walk approximation of the solution of a Markovian BSDE whose terminal condition is a locally H{\"o}lder 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.
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Donsker-Type Theorem for BSDEs: Rate of Convergence
The random walk approximation for Markovian BSDEs converges in Wasserstein distance at rate n^{-(α∧ε/2)}, improving n^{-ε/4} and reaching the CLT-optimal n^{-1/2} for Lipschitz data.
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