Strong Approximations of BSDEs in a domain
نویسنده
چکیده
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 [4, 29]. 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 −ε where h denotes the time step and ε is any positive parameter. This rate corresponds to the strong exit time approximation. It is improved to h 1 2 −ε 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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