Large deviations for occupation and waiting times of infinite ergodic transformations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918331262435328 |
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| author | Sera, Toru |
| author_facet | Sera, Toru |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02658 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large deviations for occupation and waiting times of infinite ergodic transformations Sera, Toru Dynamical Systems Probability Primary 37A40, Secondary 37A50, 60F10 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. |
| title | Large deviations for occupation and waiting times of infinite ergodic transformations |
| topic | Dynamical Systems Probability Primary 37A40, Secondary 37A50, 60F10 |
| url | https://arxiv.org/abs/2403.02658 |