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 $\mathbb{R}^d$. Our technique, in the innite 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 coeffcient, and our proof involves accurate properties of last passage times at 0 of one dimensional semimartingales.
Citation
Frédéric Bernardin. Mireille Bossy. Miguel Martinez. Denis Talay. "On mean numbers of passage times in small balls of discretized Itô processes." Electron. Commun. Probab. 14 302 - 316, 2009. https://doi.org/10.1214/ECP.v14-1479
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