# Strong Approximations of BSDEs in a domain

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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.
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https://hal.archives-ouvertes.fr/hal-00177481
Contributor : Stephane Menozzi <>
Submitted on : Monday, September 15, 2008 - 11:39:15 AM
Last modification on : Sunday, March 31, 2019 - 1:23:25 AM
Long-term archiving on : Tuesday, September 21, 2010 - 5:13:27 PM

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### Citation

Bruno Bouchard, Stephane Menozzi. Strong Approximations of BSDEs in a domain. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2009, 15 (4), pp.1117-1147. ⟨10.3150/08-BEJ181⟩. ⟨hal-00177481v2⟩

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