The singularity spectrum of Lévy processes in multifractal time

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A pure jump Markov process with a random singularity spectrum (2009, background): “Though it is easy to construct artificial ad hoc processes that do not satisfy these properties, it is remarkable that many “natural” processes of very different kind follow this rule: Lévy processes [16], Lévy processes in multifractal time [5], fractional Brownian motions, random self-similar meas”
Gaussian multiplicative chaos and applications: A review (2013, background): “A quite simple and concise proof of the above theorem is gathered in the appendix and, to our knowledge, is new in such generality (though much more is known in dimension 1: see [14, 24]).”