On the Besov-Orlicz path regularity of some Gaussian processes

TL;DR

This paper establishes Besov-Orlicz regularity of sample paths for various Gaussian processes using additive decomposition and properties of fractional Brownian motion.

Contribution

It provides a unified, direct proof of regularity for a broad class of Gaussian processes, including bifractional and subfractional Brownian motions.

Findings

Proves Besov-Orlicz regularity for bifractional Brownian motion with specific parameters.

Establishes regularity results for subfractional Brownian motion.

Includes certain self-similar processes in the regularity analysis.

Abstract

In this paper, we rely on the additive decomposition in law satisfied by a class of stochastic processes, combined with the well-known regulariy properties of fractional Brownian motion, to establish Besov-Orlicz regularity of their sample paths. This provides a unified and direct proof for a broad class of processes, including bifractional Brownian motion with parameters $H\in (0, 1]$, $ K\in (0, 2)$ such that $HK \in (0, 1)$, subfractional Brownian motion with Hurst parameter $H\in (0, 1)$, and certain class of self-similar processes. %associated with the stochastic heat equation.