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Different possible behaviors of wavelet leaders of the Brownian motion

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  • Ayache, Antoine
  • Esser, Céline
  • Kleyntssens, Thomas

Abstract

The aim of this paper is to prove that wavelet leaders allow to get very fine properties of the trajectories of the Brownian motion: we show that the three well-known behaviors of its oscillations, namely to be ordinary, rapid and slow, are also present in the behavior of the size of its wavelet leaders.

Suggested Citation

  • Ayache, Antoine & Esser, Céline & Kleyntssens, Thomas, 2019. "Different possible behaviors of wavelet leaders of the Brownian motion," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 54-60.
    • Handle: RePEc:eee:stapro:v:150:y:2019:i:c:p:54-60
    DOI: 10.1016/j.spl.2019.02.003
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    References listed on IDEAS

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    1. Arneodo, A. & Bacry, E. & Muzy, J.F., 1995. "The thermodynamics of fractals revisited with wavelets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 213(1), pages 232-275.
    2. B. Lashermes & S. G. Roux & P. Abry & S. Jaffard, 2008. "Comprehensive multifractal analysis of turbulent velocity using the wavelet leaders," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 61(2), pages 201-215, January.
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    Cited by:

    1. Loosveldt, L., 2023. "Multifractional Hermite processes: Definition and first properties," Stochastic Processes and their Applications, Elsevier, vol. 165(C), pages 465-500.

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