From Multifractal Measures to Multifractal Wavelet Series

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Wavelet construction of Generalized Multifractional processes. (2007, methodology): “2) For analyzing the irregularity of a signal {X(t)}t∈Rd having a very erratic pointwise Hölder exponent, one often uses some multifractal spectrum of {X(t)}t∈Rd, for example the singularities spectrum {θX(γ)}γ∈[0,1] which is a measure of the geometric repartition of the pointwise Hölder exponents o”
Wavelet Leaders in Multifractal Analysis (2006, background): “Typical examples of wavelet series satisfying this property can be constructed starting with a probability measure μ defined on R and picking, for an α ≥ 0 and q > 0, cλ = 2 −αj[μ(λ)]q, see [10, 7] and references therein.”
The singularity spectrum of Lévy processes in multifractal time (2007, background): “Another approach consists in generating multifractal random wavelet series [23,7].”