On the double points of operator stable L\'evy processes

TL;DR

This paper calculates the Hausdorff dimension of the set of double points for symmetric operator stable Lévy processes, linking it to the eigenvalues of the process's stability exponent.

Contribution

It provides a formula for the Hausdorff dimension of double points based on the eigenvalues of the stability exponent, advancing understanding of the geometric properties of these processes.

Findings

Hausdorff dimension of double points determined

Dimension expressed via eigenvalues of stability exponent

Results apply to symmetric operator stable Lévy processes

Abstract

We determine the Hausdorff dimension of the set of double points for a symmetric operator stable L\'evy process in terms of the eigenvalues of its stability exponent.