Large deviations for occupation and waiting times of infinite ergodic transformations
arXiv:2403.02658 · doi:10.1017/etds.2025.10246
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.
32 pages