## Bernoulli

• Bernoulli
• Volume 15, Number 4 (2009), 1117-1147.

### 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 (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.

#### Article information

Source
Bernoulli, Volume 15, Number 4 (2009), 1117-1147.

Dates
First available in Project Euclid: 8 January 2010

https://projecteuclid.org/euclid.bj/1262962228

Digital Object Identifier
doi:10.3150/08-BEJ181

Mathematical Reviews number (MathSciNet)
MR2597585

Zentralblatt MATH identifier
1204.60048

#### Citation

Bouchard, Bruno; Menozzi, Stéphane. Strong approximations of BSDEs in a domain. Bernoulli 15 (2009), no. 4, 1117--1147. doi:10.3150/08-BEJ181. https://projecteuclid.org/euclid.bj/1262962228

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