State-dependent inverse-subordinator time changes of regenerative processes: Excursion structure and multiscale occupation-time limits
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866913156592304128 |
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| author | Yamato, Kosuke |
| author_facet | Yamato, Kosuke |
| contents | We study regenerative processes time-changed by state-dependent inverse subordinators. The construction assigns possibly different independent subordinators to measurable classes of excursions and builds a random clock from the corresponding occupation times. Although the resulting process is generally not regenerative, we prove that its transformed excursion point process is again Poisson, using an excursion-wise marking-and-mapping procedure. We apply this to study occupation-time asymptotics. Under regular variation assumptions on the transformed excursion lifetime tails, we prove a multiscale joint occupation-time limit theorem, including generalized arcsine laws and Darling--Kac type limits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23659 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | State-dependent inverse-subordinator time changes of regenerative processes: Excursion structure and multiscale occupation-time limits Yamato, Kosuke Probability 60G55, 60F17 We study regenerative processes time-changed by state-dependent inverse subordinators. The construction assigns possibly different independent subordinators to measurable classes of excursions and builds a random clock from the corresponding occupation times. Although the resulting process is generally not regenerative, we prove that its transformed excursion point process is again Poisson, using an excursion-wise marking-and-mapping procedure. We apply this to study occupation-time asymptotics. Under regular variation assumptions on the transformed excursion lifetime tails, we prove a multiscale joint occupation-time limit theorem, including generalized arcsine laws and Darling--Kac type limits. |
| title | State-dependent inverse-subordinator time changes of regenerative processes: Excursion structure and multiscale occupation-time limits |
| topic | Probability 60G55, 60F17 |
| url | https://arxiv.org/abs/2605.23659 |