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Transformation de Lévy et zéros du mouvement Brownien
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  • Published: June 1995

Transformation de Lévy et zéros du mouvement Brownien

  • M. Malric1 

Probability Theory and Related Fields volume 101, pages 227–236 (1995)Cite this article

Abstract

In this paper, it is shown that the iterated Lévy transforms (β n) of a standard Brownian motion β, so defined:

$$\beta ^0 = \beta ,and:\beta _t^{n + 1} = \int\limits_0^t {\operatorname{sgn} (\beta _s^n )} d\beta _s^n (n \geqq 0)$$

satisfy the following property: a.s.,β n andβ m have common zeros, as soon asm>n+1. This property bears some relation with the conjectured ergodicity of the Lévy transform.

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Référence

  1. Dubins, L., Smorodinsky, M.: The Modified, discrete, Lévy transformation is Bernoulli. In: Azéma, J., Meyer, P.A. (eds.) Sém. Probas.XXVI. (Lect. Notes Math. vol., 1526 pp. 157–161) Berlin Heidelberg New York: Springer 1992

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Authors and Affiliations

  1. Laboratoire de Probabilités, Université, P. & M. Curie, 4, Place Jussieu, Tour 56, F-75252, Paris Cedex 05, France

    M. Malric

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  1. M. Malric
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Cite this article

Malric, M. Transformation de Lévy et zéros du mouvement Brownien. Probab. Th. Rel. Fields 101, 227–236 (1995). https://doi.org/10.1007/BF01375826

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  • Received: 15 July 1993

  • Revised: 01 July 1994

  • Issue Date: June 1995

  • DOI: https://doi.org/10.1007/BF01375826

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Mathematics Subject Classification

  • 60H05
  • 60I65
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