On mean numbers of passage times in small balls of discretized Itô processes
Frédéric Bernardin, CETE de Lyon
Mireille Bossy, INRIA Sophia Antipolis Méditérannée
Miguel Martinez, Université Paris-Est Marne-la-Vallée, LAMA, UMR 8050 CNRS
Denis Talay, INRIA Sophia Antipolis Méditérannée
Abstract
The aim of this note is to prove estimates on mean values of the number of times that Itô processes observed at discrete times visit small balls in Rd. Our technique, in the in nite horizon case, is inspired by Krylov's arguments in [2, Chap.2]. In the fi nite horizon case,
motivated by an application in stochastic numerics, we discount the number of visits by a
locally exploding coeffcient, and our proof involves accurate properties of last passage times at 0 of one dimensional semimartingales.
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