Besov-Orlicz Path Regularity of Non-Gaussian Processes

Abstract

In the article, Besov-Orlicz regularity of sample paths of stochastic processes that are represented by multiple integrals of order \(n\in \mathbb {N}\) is treated. We assume that the considered processes belong to the Hölder space $$ C^{\alpha}([0,T];L^{2}({\Omega}))\quad\text{with}\quad \alpha\in (0,1), $$ and we give sufficient conditions for them to have paths in the exponential Besov-Orlicz space $$ B_{{\varPhi}_{2/n},\infty}^{\alpha}(0,T)\qquad \text{with}\qquad {\varPhi}_{2/n}(x)=\mathrm{e}^{x^{2/n}}-1. $$ These results provide an extension of what is known for scalar Gaussian stochastic processes to stochastic processes in an arbitrary finite Wiener chaos. As an application, the Besov-Orlicz path regularity of fractionally filtered Hermite processes is studied. But while the main focus is on the non-Gaussian case, some new path properties are obtained even for fractional Brownian motions.