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

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

Electron. Commun. Probab. 14, 302-316 (2009).

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

Citations:

Zbl 0459.93002