We study the H\" olderian regularity of Gaussian wavelets series and show that they display,
almost surely, three types of points: slow, ordinary and rapid. In particular, this fact holds for …

We identify three types of pointwise behaviour in the regularity of the (generalized)
Rosenblatt process. This extends to a non Gaussian setting previous results known for the …

We study the pointwise regularity of the Multifractional Brownian Motion and, in particular,
we obtain the existence of so-called slow points of the process, that is points which exhibit a …

The multifractal formalisms allow to numerically approximate the Hölder spectrum of a real-
life signal f. In this thesis, we study some multifractal formalisms based on profiles: these are …

We define multifractional Hermite processes which generalize and extend both
multifractional Brownian motion and Hermite processes. It is done by substituting the Hurst …

The topics of this thesis lie at the interference of probability theory with dimensional and
harmonic analysis, accentuating the geometric properties of random paths of Gaussian and …