H\"older continuity of the convex minorant of a L\'evy process

TL;DR

This paper characterizes the H"older continuity of the convex minorant of L"evy processes, linking path properties at zero with the boundedness of slope sets, advancing understanding of their regularity.

Contribution

It introduces a novel connection between the path behavior of L"evy processes at zero and the boundedness of the convex minorant's slopes, providing new insights into their regularity.

Findings

Characterizes H"older continuity of convex minorant for most L"evy processes

Establishes a link between path properties at zero and slope boundedness

Provides a new method to analyze regularity of L"evy process convex minorants

Abstract

We characterise the H\"older continuity of the convex minorant of most L\'evy processes. The proof is based on a novel connection between the path properties of the L\'evy process at zero and the boundedness of the set of $r$-slopes of the convex minorant.