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 Electronic Communications in Probability > Vol. 14 (2009) > Paper 30 open journal systems 


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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Pages: 302-316

Published on: July 25, 2009


Bibliography
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Electronic Communications in Probability. ISSN: 1083-589X