Large deviations for occupation and waiting times of infinite ergodic transformations

2024/03/05 by Sera, Toru · 1 citation
#60F10 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37A40 #Probability (math.PR) #Secondary 37A50

paper · doi:10.48550/arxiv.2403.02658

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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