Regularity of paths of stochastic measures

TL;DR

This paper investigates the regularity of paths generated by stochastic measures, establishing Besov regularity and Fourier series expansions under weaker conditions than previous studies.

Contribution

It provides new proofs of Besov regularity and Fourier series expansions for paths of stochastic measures with less restrictive assumptions.

Findings

Paths of stochastic measures have Besov regularity.

Fourier series expansion of stochastic measure paths is established.

Results hold under weaker conditions than prior work.

Abstract

Random functions $\mu(x)$, generated by values of stochastic measures are considered. The Besov regularity of the continuous paths of $\mu(x)$, $x\in[0,1]^d$ is proved. Fourier series expansion of $\mu(x)$, $x\in[0,2\pi]$ is obtained. These results are proved under weaker conditions than similar results in previous papers.