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Convex minorants and the fluctuation theory of Lévy processes
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González Cázares, Jorge Ignacio and Mijatović, Aleksandar (2022) Convex minorants and the fluctuation theory of Lévy processes. Latin American Journal of Probability and Mathematical Statistics, 19 (1). pp. 983-999. doi:10.30757/ALEA.v19-39 ISSN 1980-0436.
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Official URL: http://dx.doi.org/10.30757/ALEA.v19-39
Abstract
We establish a novel characterisation of the law of the convex minorant of any Lévy process. Our self-contained elementary proof is based on the analysis of piecewise linear convex functions and requires only very basic properties of Lévy processes. Our main result provides a new
simple and self-contained approach to the fluctuation theory of Lévy processes, circumventing local time and excursion theory. Easy corollaries include classical theorems, such as Rogozin’s regularity criterion, Spitzer’s identities and the Wiener-Hopf factorisation, as well as a novel factorisation identity
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
| Journal or Publication Title: | Latin American Journal of Probability and Mathematical Statistics | ||||
| Publisher: | Instituto Nacional de Matemáticas Pura e Aplicada | ||||
| ISSN: | 1980-0436 | ||||
| Official Date: | 23 June 2022 | ||||
| Dates: |
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| Volume: | 19 | ||||
| Number: | 1 | ||||
| Page Range: | pp. 983-999 | ||||
| DOI: | 10.30757/ALEA.v19-39 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Open Access (Creative Commons) |
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