## Electronic Communications in Probability

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

#### 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.

#### Article information

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

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

https://projecteuclid.org/euclid.ecp/1465234739

Digital Object Identifier
doi:10.1214/ECP.v14-1479

Mathematical Reviews number (MathSciNet)
MR2524981

Zentralblatt MATH identifier
1189.60108

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

Rights

#### Citation

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

#### References

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