Strong approximations of BSDEs in a domain
Bruno Bouchard and Stéphane Menozzi
Source: Bernoulli Volume 15, Number 4
(2009), 1117-1147.
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 (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 h1/4−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 h1/2−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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Permanent link to this document: http://projecteuclid.org/euclid.bj/1262962228
Digital Object Identifier: doi:10.3150/08-BEJ181
Zentralblatt MATH identifier: 05816134
Mathematical Reviews number (MathSciNet): MR2597585
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