Electronic Communications in Probability

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

Frédéric Bernardin, Mireille Bossy, Miguel Martinez, and Denis Talay

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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.

Article information

Electron. Commun. Probab., Volume 14 (2009), paper no. 30, 302-316.

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

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Primary: 60G99: None of the above, but in this section

Diffusion processes sojourn times estimates discrete times

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Bernardin, Frédéric; Bossy, Mireille; Martinez, Miguel; Talay, Denis. On mean numbers of passage times in small balls of discretized Itô processes. Electron. Commun. Probab. 14 (2009), paper no. 30, 302--316. doi:10.1214/ECP.v14-1479. https://projecteuclid.org/euclid.ecp/1465234739

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