Large deviations for occupation and waiting times of infinite ergodic transformations
Dynamical Systems
2026-02-11 v2 Probability
Abstract
We establish large deviation estimates related to the Darling--Kac theorem and generalized arcsine laws for occupation and waiting times of ergodic transformations preserving an infinite measure, such as non-uniformly expanding interval maps with indifferent fixed points. For the proof, we imitate the study of generalized arcsine laws for occupation times of one-dimensional diffusion processes and adopt a method of double Laplace transform.
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Cite
@article{arxiv.2403.02658,
title = {Large deviations for occupation and waiting times of infinite ergodic transformations},
author = {Toru Sera},
journal= {arXiv preprint arXiv:2403.02658},
year = {2026}
}
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32 pages