Open Access
2009 On mean numbers of passage times in small balls of discretized Itô processes
Frédéric Bernardin, Mireille Bossy, Miguel Martinez, Denis Talay
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Electron. Commun. Probab. 14: 302-316 (2009). DOI: 10.1214/ECP.v14-1479


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.


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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." Electron. Commun. Probab. 14 302 - 316, 2009.


Accepted: 25 July 2009; Published: 2009
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60108
MathSciNet: MR2524981
Digital Object Identifier: 10.1214/ECP.v14-1479

Primary: 60G99

Keywords: Diffusion processes , discrete times , estimates , sojourn times

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