In this note, we recall main properties of generalized random fields and present a proof of
the continuity theorem of Paul L\'evy for generalized random fields in the space of tempered …

We address estimation of parametric coefficients of a pure-jump Lévy driven univariate
stochastic differential equation (SDE) model, which is observed at high frequency over a …

We consider a large class of shallow neural networks with randomly initialized parameters
and rectified linear unit activation functions. We prove that these random neural networks …

We identify a necessary and sufficient condition for a Lévy white noise to be a tempered
distribution. More precisely, we show that if the Lévy measure associated with this noise has …

In this paper, we study the Besov regularity of a general d-dimensional Lévy white noise.
More precisely, we describe new sample paths properties of a given noise in terms of …

In this paper, we study the Besov regularity of Lévy white noises on the d-dimensional torus.
Due to their rough sample paths, the white noises that we consider are defined as …

Characteristic functionals are one of the main analytical tools used to quantify the statistical
properties of random fields and generalized random fields. The viewpoint taken here is that …

We characterize the local smoothness and the asymptotic growth rate of the Lévy white
noise. We do so by characterizing the weighted Besov spaces in which it is located. We …

We propose a systematic construction of native Banach spaces for general spline-
admissible operators ${\rm L} $. In short, the native space for ${\rm L} $ and the (dual) norm …

The sample paths of white noise are proved to be elements of certain Besov spaces with
dominating mixed smoothness. Unlike in isotropic spaces, here the regularity does not get …