Abstract
We establish general moment estimates for the discrete and continuous exit times of a general Itô process in terms of the distance to the boundary. These estimates serve as intermediate steps to obtain strong convergence results for the approximation of a continuous exit time by a discrete counterpart, computed on a grid. In particular, we prove that the discrete exit time of the Euler scheme of a diffusion converges in the ${\mathbf{L}}_{1}$ norm with an order $1/2$ with respect to the mesh size. This rate is optimal.
Citation
Bruno Bouchard. Stefan Geiss. Emmanuel Gobet. "First time to exit of a continuous Itô process: General moment estimates and ${\mathrm{L}}_{1}$-convergence rate for discrete time approximations." Bernoulli 23 (3) 1631 - 1662, August 2017. https://doi.org/10.3150/15-BEJ791
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