On mean numbers of passage times in small balls of discretized Itô processes

Frédéric Bernardin 1 Mireille Bossy 2 Miguel Martinez 3 Denis Talay 2
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : The aim of this note is to prove estimates on mean values of the number of times that Itô pro- cesses observed at discrete times visit small balls in Rd. Our technique, in the infinite horizon case, is inspired by Krylov's arguments in [2, Chap.2]. In the finite horizon case, motivated by an application in stochastic numerics, we discount the number of visits by a locally exploding coef- ficient, and our proof involves accurate properties of last passage times at 0 of one dimensional semimartingales.
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Submitted on : Tuesday, June 21, 2011 - 2:04:32 PM
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  • HAL Id : hal-00602053, version 1


Frédéric Bernardin, Mireille Bossy, Miguel Martinez, Denis Talay. On mean numbers of passage times in small balls of discretized Itô processes. Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2009, 14, pp.302-316. ⟨hal-00602053⟩



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