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Journal Articles Electronic Communications in Probability Year : 2009

On mean discounted numbers of passage times in small balls of Ito processes observed at discrete times

Mireille Bossy
Denis Talay
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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 $\er^d$. 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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Dates and versions

inria-00347610 , version 1 (16-12-2008)
inria-00347610 , version 2 (27-01-2009)
inria-00347610 , version 3 (09-05-2009)

Identifiers

  • HAL Id : inria-00347610 , version 3

Cite

Frédéric Bernardin, Mireille Bossy, Miguel Martinez, Denis Talay. On mean discounted numbers of passage times in small balls of Ito processes observed at discrete times. Electronic Communications in Probability, 2009, 14, pp.19. ⟨inria-00347610v3⟩
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