  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 (H{\"o}lder, 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.

Classical Analysis and ODEs;Numerical Analysis;Functional Analysis;Numerical Analysis