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.
Acknowledgments
JGC and AM are supported by the EPSRC grant EP/V009478/1 and The Alan Turing Institute under the EPSRC grant EP/N510129/1; AM was also supported by the EPSRC grant EP/W006227/1 and the Turing Fellowship funded by the Programme on Data-Centric Engineering of Lloyd’s Register Foundation; DKB is funded by the CDT in Mathematics and Statistics at The University of Warwick. All three authors would like to thank the Isaac Newton Institute for Mathematical Sciences in Cambridge, supported by EPSRC grant EP/R014604/1, for hospitality during the programme on Fractional Differential Equations where part of this work was undertaken. We also want to thank the anonymous referees whose questions led us to complete the characterisation in the case .
Citation
Jorge González Cázares. David Kramer-Bang. Aleksandar Mijatović. "Hölder continuity of the convex minorant of a Lévy process." Electron. Commun. Probab. 28 1 - 12, 2023. https://doi.org/10.1214/23-ECP549
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