Characterization of p-exponents by continuous wavelet transforms, applications to the multifractal analysis of sum of random pulses

05/30/2023

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by   Guillaume Saës, et al.

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The theory of orthonormal wavelet bases is a useful tool in multifractal analysis, as it provides a characterization of the different exponents of pointwise regularities (Hölder, p-exponent, lacunarity, oscillation, etc.). However, for some homogeneous self-similar processes, such as sums of random pulses (sums of regular, well-localized functions whose expansions and translations are random), it is easier to estimate the spectrum using continuous wavelet transforms. In this article, we present a new characterization of p-exponents by continuous wavelet transforms and we provide an application to the regularity analysis of sums of random pulses.