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# Strong Approximations of BSDEs in a domain

## Abstract

We study the strong approximation of a Backward SDE with finite stopping time horizon, namely the first exit time of a forward SDE from a cylindrical domain. We use the Euler scheme approach of Bouchard and Touzi, Zhang 04}. When the domain is piecewise smooth and under a non-characteristic boundary condition, we show that the associated strong error is at most of order $h^{\frac14-\eps}$ where $h$ denotes the time step and $\eps$ is any positive parameter. This rate corresponds to the strong exit time approximation. It is improved to $h^{\frac12-\eps}$ when the exit time can be exactly simulated or for a weaker form of the approximation error. Importantly, these results are obtained without uniform ellipticity condition.Comment: 35 page

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This paper was published in arXiv.org e-Print Archive.

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