## On mean numbers of passage times in small balls of discretized Itô processes.(English)Zbl 1189.60108

Summary: 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 in nite horizon case, is inspired by Krylov’s arguments in [Controlled diffusion processes. Transl. by A. B. Aries. Applications of Mathematics, Vol. 14. Springer (1980; Zbl 0459.93002)]. In the fi nite 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.

### MSC:

 60G99 Stochastic processes

### Keywords:

diffusion processes; sojourn times; estimates; discrete times

Zbl 0459.93002
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