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Large deviations for occupation and waiting times of infinite ergodic transformations (2403.02658v2)
Published 5 Mar 2024 in math.DS and math.PR
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.