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The theory of orthonormal wavelet bases is a useful tool in multifractalanalysis, as it provides a characterization of the different exponents ofpointwise regularities (H{\"o}lder, p-exponent, lacunarity, oscillation, etc.).However, for some homogeneous self-similar processes, such as sums of randompulses (sums of regular, well-localized functions whose expansions andtranslations are random), it is easier to estimate the spectrum usingcontinuous wavelet transforms. In this article, we present a newcharacterization of p-exponents by continuous wavelet transforms and we providean application to the regularity analysis of sums of random pulses.

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