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Multifractal analysis of sums of random pulses

Part of: Classical measure theory Real functions

Published online by Cambridge University Press:  22 June 2023

GUILLAUME SAËS  and
STÉPHANE SEURET
GUILLAUME SAËS
Affiliation:
Laboratoire d’Analyse et de Mathématiques appliquées, Université Paris-Est Créteil, Créteil, France. e-mails: guillaume.saes@u-pec.fr, seuret@u-pec.fr
STÉPHANE SEURET
Affiliation:
Laboratoire d’Analyse et de Mathématiques appliquées, Université Paris-Est Créteil, Créteil, France. e-mails: guillaume.saes@u-pec.fr, seuret@u-pec.fr
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Abstract

In this paper, we investigate the regularity properties and determine the almost sure multifractal spectrum of a class of random functions constructed as sums of pulses with random dilations and translations. In addition, the continuity moduli of the sample paths of these stochastic processes are investigated.

MSC classification

Primary: 28A80: Fractals 28A78: Hausdorff and packing measures 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 175 , Issue 3 , November 2023 , pp. 569 - 593
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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