This analysis demonstrates large deviation estimates in ergodic transformations, suggesting implications for occupation and waiting times.
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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Toru Sera (2025) studied this question.
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