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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.
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https://hal.archives-ouvertes.fr/hal-00177481
Contributor : Stephane Menozzi <>
Submitted on : Monday, October 8, 2007 - 12:22:42 PM
Last modification on : Thursday, March 26, 2020 - 9:14:30 PM
Document(s) archivé(s) le : Sunday, April 11, 2010 - 10:24:45 PM

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  • HAL Id : hal-00177481, version 1
  • ARXIV : 0710.1519

Citation

Bruno Bouchard, Stephane Menozzi. Strong Approximations of BSDEs in a domain. 2007. ⟨hal-00177481v1⟩

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