PreprintCC BY-SA 4.0arXiv
Infinite-variation Lévy processes are either strongly eroded or abrupt
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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BibTeX
@misc{cazares2026infinitevariation,
title = {{Infinite-variation Lévy processes are either strongly eroded or abrupt}},
author = {Jorge González Cázares and David Kramer-Bang and Aleksandar Mijatović},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20916},
eprint = {2610.20916},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20916},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Infinite-variation Lévy processes are either strongly eroded or abrupt
AU - Jorge González Cázares
AU - David Kramer-Bang
AU - Aleksandar Mijatović
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20916
UR - https://arxiv.org/abs/2610.20916
AB - 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.
ER -