Multifractal analysis of sums of random pulses
Guillaume Saes (UPEC UP12), St\'ephane Seuret (UPEC UP12)
TL;DR
This paper investigates the multifractal spectrum and continuity properties of a class of random functions formed by summing pulses with random dilations and translations, providing insights into their complex fractal structure.
Contribution
It introduces a novel analysis of the multifractal spectrum and continuity modulii for sums of random pulses, expanding understanding of their fractal behavior.
Findings
Determined the almost sure multifractal spectrum of the functions.
Analyzed the continuity modulii of the constructed functions.
Provided new insights into the fractal properties of random pulse sums.
Abstract
In this paper, we 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 modulii of these functions is investigated.
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Taxonomy
TopicsComplex Systems and Time Series Analysis