First time to exit of a continuous It\^{o} process: general moment estimates and $L_1$-convergence rate for discrete time approximations - Département de mathématiques appliquées Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2013

First time to exit of a continuous It\^{o} process: general moment estimates and $L_1$-convergence rate for discrete time approximations

Résumé

We establish general moment estimates for the discrete and continuous exit times of a general It\^{o} 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 $L_1$ 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)

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Bruno Bouchard, Stefan Geiss, Emmanuel Gobet. First time to exit of a continuous It\^{o} process: general moment estimates and $L_1$-convergence rate for discrete time approximations. 2013. ⟨hal-00844887v1⟩
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