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November 2009 Strong approximations of BSDEs in a domain
Bruno Bouchard, Stéphane Menozzi
Bernoulli 15(4): 1117-1147 (November 2009). DOI: 10.3150/08-BEJ181


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 (Stochastic Process. Appl. 111 (2004) 175–206 and Ann. Appl. Probab. 14 (2004) 459–488). 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 $h^{1/4−ɛ}$, where $h$ denotes the time step and $ɛ$ is any positive parameter. This rate corresponds to the strong exit time approximation. It is improved to $h^{1/2−ɛ}$ 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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Bruno Bouchard. Stéphane Menozzi. "Strong approximations of BSDEs in a domain." Bernoulli 15 (4) 1117 - 1147, November 2009.


Published: November 2009
First available in Project Euclid: 8 January 2010

zbMATH: 1204.60048
MathSciNet: MR2597585
Digital Object Identifier: 10.3150/08-BEJ181

Rights: Copyright © 2009 Bernoulli Society for Mathematical Statistics and Probability


Vol.15 • No. 4 • November 2009
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