Limit laws for random walks in a dynamic path-cone mixing random environment
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912126899060736 |
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| author | Bethuelsen, Stein Andreas Völlering, Florian |
| author_facet | Bethuelsen, Stein Andreas Völlering, Florian |
| contents | We study the asymptotic behaviour of a random walk whose evolution is dependent on the state of an itself dynamically evolving environment. In particular, we extend our previous results in [Bethuelsen and Völlering, 2016] and prove a strong law of large numbers and large deviation estimates assuming that the dynamic environment is "path-cone"-mixing. Under a mild assumption on the decay rate of this mixing property we further obtain a functional central limit theorem under the annealed law. Our method of proofs rest on the study of the so-called local environment process and general results for $ϕ$-mixing stochastic processes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_06756 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Limit laws for random walks in a dynamic path-cone mixing random environment Bethuelsen, Stein Andreas Völlering, Florian Probability We study the asymptotic behaviour of a random walk whose evolution is dependent on the state of an itself dynamically evolving environment. In particular, we extend our previous results in [Bethuelsen and Völlering, 2016] and prove a strong law of large numbers and large deviation estimates assuming that the dynamic environment is "path-cone"-mixing. Under a mild assumption on the decay rate of this mixing property we further obtain a functional central limit theorem under the annealed law. Our method of proofs rest on the study of the so-called local environment process and general results for $ϕ$-mixing stochastic processes. |
| title | Limit laws for random walks in a dynamic path-cone mixing random environment |
| topic | Probability |
| url | https://arxiv.org/abs/2303.06756 |