Statistical properties for mixing Markov chains with applications to dynamical systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912484358619136 |
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| author | Cai, Ao Duarte, Pedro Klein, Silvius |
| author_facet | Cai, Ao Duarte, Pedro Klein, Silvius |
| contents | We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product encoding a random torus translation, a model we call a mixed random-quasiperiodic dynamical system. This abstract scheme is applicable to many other types of skew product dynamics, including systems for which the spectral gap property for the transition or the transfer operator does not hold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_16908 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Statistical properties for mixing Markov chains with applications to dynamical systems Cai, Ao Duarte, Pedro Klein, Silvius Dynamical Systems Probability We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product encoding a random torus translation, a model we call a mixed random-quasiperiodic dynamical system. This abstract scheme is applicable to many other types of skew product dynamics, including systems for which the spectral gap property for the transition or the transfer operator does not hold. |
| title | Statistical properties for mixing Markov chains with applications to dynamical systems |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2210.16908 |