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Article Dans Une Revue Bernoulli Année : 2017

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

Résumé

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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Dates et versions

hal-00844887 , version 1 (16-07-2013)
hal-00844887 , version 2 (09-09-2014)

Identifiants

Citer

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, 2017, 23 (3), pp.1631-1662. ⟨10.3150/15-BEJ791⟩. ⟨hal-00844887v2⟩
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