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Article Dans Une Revue Electronic Communications in Probability Année : 2009

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

Résumé

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 $mathbb{R}^d$. 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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Dates et versions

hal-00602053 , version 1 (28-06-2021)

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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, 2009, 14, pp.302-316. ⟨10.1214/ecp.v14-1479⟩. ⟨hal-00602053⟩
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