Donsker-type theorem for BSDEs: Rate of convergence

Philippe Briand; Christel Geiss; Stefan Geiss; Céline Labart

doi:10.3150/20-BEJ1259

May 2021 Donsker-type theorem for BSDEs: Rate of convergence

Philippe Briand, Christel Geiss, Stefan Geiss, Céline Labart

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Abstract

In this paper, we study in the Markovian case the rate of convergence in Wasserstein distance when the solution to a BSDE is approximated by a solution to a BSDE driven by a scaled random walk as introduced in Briand, Delyon and Mémin (Electron. Commun. Probab. 6 (2001) Art. ID 1). This is related to the approximation of solutions to semilinear second order parabolic PDEs by solutions to their associated finite difference schemes and the speed of convergence.

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Philippe Briand. Christel Geiss. Stefan Geiss. Céline Labart. "Donsker-type theorem for BSDEs: Rate of convergence." Bernoulli 27 (2) 899 - 929, May 2021. https://doi.org/10.3150/20-BEJ1259

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Received: 1 July 2019; Revised: 1 July 2020; Published: May 2021

First available in Project Euclid: 24 March 2021

Digital Object Identifier: 10.3150/20-BEJ1259

Keywords: Backward stochastic differential equations , convergence rate , Donsker’s theorem , finite difference scheme , scaled random walk , Wasserstein distance

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