Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

Abstract: We establish the Besov-Orlicz path regularity of the Lei-Nualart process. This immediately implies that any Gaussian process admitting a decomposition in law as the sum of a fractional Brownian motion and a Lei-Nualart process inherits the Besov-Orlicz regularity of its fractional Brownian motion component. We illustrate this transfer for the bi-fractional Brownian motion with parameters $ H \in (0, 1), K \in (0, 2)$ such that $HK \in (0, 1)$, the sub-fractional Brownian motion with Hurst parameter $H \in (0, 1)$, and a class of self-similar Gaussian processes introduced by Harnett and Nualart.