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 ∈ N is treated. We give sufficient conditions for the considered processes to have paths in the exponential Besov-Orlicz spaceThese 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.