# UN PROCESSUS PONCTUEL ASSOCIÉ AUX MAXIMA LOCAUX DU MOUVEMENT BROWNIEN

Abstract : Let $B = (B_t)_{t \in \rrf}$ be a symmetric brownian motion, so $(B_t)_{t \in \rrf_+}$ and $(B_{-t})_{t \in \rrf_+}$ are indépendent brownian motions. Given $a \ge b>0$, we give the law of the random set ${\cal M}_{a,b} = \{t \in {\bf R} : B_t = \max_{s \in [t-a,t+b]} B_s\}.$ Using the relation connecting this set with the closed regenerative set ${\cal R}_a = \{t \in {\bf R}_+ : B_t = \max_{s \in [(t-a)_+,t]} B_s\},$ we describe the Lévy measure of a subordinator whose closed range is ${\cal R}_a$.
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Cited literature [9 references]

https://hal.archives-ouvertes.fr/hal-00294870
Contributor : Christophe Leuridan <>
Submitted on : Thursday, July 10, 2008 - 5:35:34 PM
Last modification on : Tuesday, February 20, 2018 - 11:10:02 AM
Long-term archiving on : Friday, May 28, 2010 - 11:24:10 PM

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• HAL Id : hal-00294870, version 1

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Christophe Leuridan. UN PROCESSUS PONCTUEL ASSOCIÉ AUX MAXIMA LOCAUX DU MOUVEMENT BROWNIEN. Probability Theory and Related Fields, Springer Verlag, 2010, 148 (3-4), pp.457-477. ⟨hal-00294870⟩

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