On mean discounted numbers of passage times in small balls of Ito processes observed at discrete times
Résumé
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 $\er^d$. Our technique, in the infinite horizon case, is inspired by Krylov's arguments in~\cite[Chap.2]{kry80}. In the finite horizon case, motivated by an application in stochastic numerics, we discount the number of visits by a locally exploding coefficient, and our proof involves accurate properties of last passage times at 0 of one dimensional semimartingales.
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