Singularity sets of Levy processes

TL;DR

This paper characterizes the size and intersection properties of the singularity sets of Levy processes and related functions, providing a comprehensive understanding of their regularity and irregularity features.

Contribution

It offers a complete description of the size and intersection properties of Holder singularity sets for Levy processes and examines the modulus of continuity constraints for these processes.

Findings

Describes the size of singularity sets of Levy processes.

Analyzes large intersection properties of these sets.

Studies the modulus of continuity at specific times.

Abstract

We completely describe the size and large intersection properties of the Holder singularity sets of Levy processes. We also study the set of times at which a given function cannot be a modulus of continuity of a Levy process. The Holder singularity sets of the sample paths of certain random wavelet series are investigated as well.