First time to exit of a continuous Itô process: general moment estimates and L1-convergence rate for discrete time approximations

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 L1 norm with an order 1/2 with respect to the mesh size.
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Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2017, 23 (3), pp.1631-1662. 〈10.3150/15-BEJ791〉
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Soumis le : mardi 9 septembre 2014 - 19:08:48
Dernière modification le : mercredi 12 septembre 2018 - 01:28:26
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Bruno Bouchard, Stefan Geiss, Emmanuel Gobet. First time to exit of a continuous Itô process: general moment estimates and L1-convergence rate for discrete time approximations. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2017, 23 (3), pp.1631-1662. 〈10.3150/15-BEJ791〉. 〈hal-00844887v2〉

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