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

Frédéric Bernardin 1 Mireille Bossy 2 Miguel Martinez 3 Denis Talay 2
2 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
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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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, Institute of Mathematical Statistics (IMS), 2009, 14, pp.19. ⟨inria-00347610v3⟩

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