We define a large class of multifractal random measures and processes with arbitrary loginfinitely divisible exact or asymptotic scaling law. These processes generalize within a unified framework both the recently defined log-normal Multifractal Random Walk processes (MRW) [33, 3] and the log-Poisson “product of cynlindrical pulses” [7]. Their construction involves some “continuous stochastic m...

We use a recently developed a priori theory of diffusion-limited aggregation (DLA) to compute multifractal dimensions and their fluctuations, using methods analogous to field theoretical resummations. There are two regimes, depending upon n, the number of particles in the DLA cluster, as well as on the multifractal moment q. In the strongly fluctuating regime quenched and annealed dimensions di...

Irregularities in the amplitude and period are characteristic of both normal and pathological sustained vowels; they are a product of perturbations inherent in the phonation process. Their analysis provides useful diagnostic information for several vocal pathologies, and their accurate modelling has been shown to improve the quality of synthesized voice. In this work, we propose the application...

Ozone is a secondary pollutant that, at high concentrations in urban environment, affects human health. Thus, suitable knowledge of ozone dynamics is essential for avoiding undesirable effects on the population. Ten-minute ozone concentration time series recorded at Córdoba (southern Spain) in 2007, for January, April, July and October, have been analysed by using the strange attractor multifra...

This paper demonstrates that the Joint Probability Distribution (JPD) of a Bayesian network is a random multinomial multifractal. With sufficient asymmetry in individual prior and conditional probability distributions, the JPD is not only highly skewed as shown by Druzdzel [3], but also is stochastically self-similar and has clusters of highprobability instantiations at all scales. Based on the...

The large deviation multifractal spectrum is a function of central importance in multifractal analysis. It allows a ne description of the distribution of the singularities of a function over a given domain. The 2-microlocal spectrum, on the other hand, provides an extremely precise picture of the regularity of a distribution at a point. These two spectra display a number of similarities: their ...

In this work, we investigate the fine regularity of Lévy processes using the 2-microlocal formalism. This framework allows us to refine the multifractal spectrum determined by Jaffard and, in addition, study the oscillating singularities of Lévy processes. The fractal structure of the latter is proved to be more complex than the classic multifractal spectrum and is determined in the case of alp...