Maxima of stationary systems of randomly time-changed Lévy particles
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910125127630848 |
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| author | Scheffel, Ioan |
| author_facet | Scheffel, Ioan |
| contents | We construct stationary max-infinitely divisible (max-id) processes from systems of randomly time-changed Lévy particles. Classical examples without time change, such as the Brown-Resnick process, are, up to marginal transformations, max-stable. We show that random time change of the underlying particles alters the dependence structure of the max-id process and leads, in general, beyond the max-stable setting. At the same time, stationarity is preserved by a suitable reconfiguration of the starting points of the particle system. We then prove that the extremal behavior of the resulting max-id process is linked to an associated max-stable Lévy-Brown-Resnick process through the max-domain of attraction (MDA). Thus, our work combines potential theory for Markov processes and extreme value theory to yield a large class of new, non-trivial stationary processes in the MDA of a given Lévy-Brown-Resnick process. So far, specific examples of processes in the MDA are scarce in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11434 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maxima of stationary systems of randomly time-changed Lévy particles Scheffel, Ioan Probability Primary 60G70, 60G10, secondary 60G51, 60G55, 60J55 We construct stationary max-infinitely divisible (max-id) processes from systems of randomly time-changed Lévy particles. Classical examples without time change, such as the Brown-Resnick process, are, up to marginal transformations, max-stable. We show that random time change of the underlying particles alters the dependence structure of the max-id process and leads, in general, beyond the max-stable setting. At the same time, stationarity is preserved by a suitable reconfiguration of the starting points of the particle system. We then prove that the extremal behavior of the resulting max-id process is linked to an associated max-stable Lévy-Brown-Resnick process through the max-domain of attraction (MDA). Thus, our work combines potential theory for Markov processes and extreme value theory to yield a large class of new, non-trivial stationary processes in the MDA of a given Lévy-Brown-Resnick process. So far, specific examples of processes in the MDA are scarce in the literature. |
| title | Maxima of stationary systems of randomly time-changed Lévy particles |
| topic | Probability Primary 60G70, 60G10, secondary 60G51, 60G55, 60J55 |
| url | https://arxiv.org/abs/2604.11434 |