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Un processus ponctuel associé aux maxima locaux du mouvement brownien
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  • Published: 19 June 2009

Un processus ponctuel associé aux maxima locaux du mouvement brownien

  • Christophe Leuridan1 

Probability Theory and Related Fields volume 148, pages 457–477 (2010)Cite this article

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Résumé

Soit \({B = (B_t)_{t \in {\bf R}}}\) un mouvement brownien symétrique, c’est-à-dire un processus tel que \({(B_t)_{t \in {\bf R}_+}}\) et \({(B_{-t})_{t \in {\bf R}_+}}\) sont deux mouvements browniens indépendants issus de 0. Pour a ≥ b > 0 fixés, nous décrivons la loi de l’ensemble

$$\mathcal{M}_{a,b} =\left\{t \in {\bf R} : B_t = \max_{s \in [t-a,t+b]}\,B_s\right\}.$$

Nous relions cet ensemble au fermé régénératif

$$\mathcal{R}_a = \left\{t \in {\bf R}_+ : B_t = \max_{s \in [(t-a)_+,t]}B_s\right\},$$

et nous donnons la mesure de Lévy d’un subordinateur dont l’image fermée est \({\mathcal{R}_a}\) .

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Author information

Authors and Affiliations

  1. Laboratoire de Mathématiques, Institut Fourier, UMR5582 (UJF-CNRS), BP 74, 38402, St Martin D’hères Cedex, France

    Christophe Leuridan

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  1. Christophe Leuridan
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Correspondence to Christophe Leuridan.

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Leuridan, C. Un processus ponctuel associé aux maxima locaux du mouvement brownien. Probab. Theory Relat. Fields 148, 457–477 (2010). https://doi.org/10.1007/s00440-009-0236-4

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  • Received: 16 May 2008

  • Revised: 30 May 2009

  • Published: 19 June 2009

  • Issue Date: November 2010

  • DOI: https://doi.org/10.1007/s00440-009-0236-4

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Mots-clés

  • Mouvement brownien
  • Maximum local
  • Processus ponctuel
  • Renouvellement
  • Fermé régénératif
  • Subordinateur

Classification Mathématique

  • 60J65
  • 60G55
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