Hölder continuity of the convex minorant of a Lévy process

Abstract

We characterise the Hölder continuity of the convex minorant of most Lévy processes. The proof is based on a novel connection between the path properties of the Lévy process at zero and the boundedness of the set of $r$-slopes of the convex minorant.

12 pages, short YouTube presentation: https://youtu.be/PKvSg2tKqfs. This version gives a complete characterisation of the Hölder continuity in terms of the Blumenthal-Getoor index when it is less than 2, improving the original result. The paper will appear in ECP