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arXiv · 2610.20916

Infinite-variation Lévy processes are either strongly eroded or abrupt

Jorge González Cázares·David Kramer-Bang·Aleksandar Mijatović
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Abstract

We prove that every real Lévy process of infinite variation is either abrupt or strongly eroded, resolving the conjectured geometric dichotomy on the smoothness of the convex hull of the graph of a Lévy path [Ann. Inst. H. Poincaré Probab. Stat. 60(4) (2024), 2352-2381]. We give counterexamples to the stronger point-hitting conjecture of Vigon. As applications, we classify convex-hull smoothness, Lipschitz-minorant contact sets and Burgers shock geometry.

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Jorge González Cázares, David Kramer-Bang, Aleksandar Mijatović. 2026-10-14. Infinite-variation Lévy processes are either strongly eroded or abrupt. https://arxiv.org/abs/2610.20916

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