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Multifractal products of cylindrical pulses
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  • Published: November 2002

Multifractal products of cylindrical pulses

  • Julien Barral1 &
  • Benoît B. Mandelbrot2 

Probability Theory and Related Fields volume 124, pages 409–430 (2002)Cite this article

  • 189 Accesses

  • 148 Citations

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Abstract.

 New multiplicative and statistically self-similar measures μ are defined on ℝ as limits of measure-valued martingales. Those martingales are constructed by multiplying random functions attached to the points of a statistically self-similar Poisson point process defined in a strip of the plane. Several fundamental problems are solved, including the non-degeneracy and the multifractal analysis of μ. On a bounded interval, the positive and negative moments of diverge under broad conditions.

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Authors and Affiliations

  1. Projet ``Fractales'', INRIA Rocquencourt, BP 150, 78153 Le Chesnay Cedex, France. e-mail: julien.barral@inria.fr, , , , , , FR

    Julien Barral

  2. Mathematics Department, Yale University, New Haven, CT 06520-8283, USA. e-mail: fractal@watson.ibm.com, , , , , , US

    Benoît B. Mandelbrot

Authors
  1. Julien Barral
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  2. Benoît B. Mandelbrot
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Additional information

First received: 14 September 1999 / Resubmited: 27 June 2001 / Revised version: 30 May 2002 / Published online: 30 September 2002

Mathematics Subject Classification (2002): 28A80, 60G18, 60G44, 60G55, 60G57

Key words or phrases: Random measures – Multifractal analysis – Continuous time martingales – Statistically self-similar Poisson point processes

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Barral, J., Mandelbrot, B. Multifractal products of cylindrical pulses. Probab Theory Relat Fields 124, 409–430 (2002). https://doi.org/10.1007/s004400200220

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  • Issue Date: November 2002

  • DOI: https://doi.org/10.1007/s004400200220

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