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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.23659 |
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Table of 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.