Limit theorems for the fluctuation of the dynamic elephant random walk in the superdiffusive case
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908366458060800 |
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| author | Tokumitsu, Go Yano, Kouji |
| author_facet | Tokumitsu, Go Yano, Kouji |
| contents | Motivated by the previous results by Coletti-de Lima-Gava-Luiz (2020) and Shiozawa (2022), we study the fluctuation of the dynamic elephant random walk in the superdiffusive case with a strong elephant component. Applying the martingale convergence theorem, we prove the Central Limit Theorem and the Law of Iterated Logarithm, where a random drift is subtracted from the process considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13810 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limit theorems for the fluctuation of the dynamic elephant random walk in the superdiffusive case Tokumitsu, Go Yano, Kouji Probability Motivated by the previous results by Coletti-de Lima-Gava-Luiz (2020) and Shiozawa (2022), we study the fluctuation of the dynamic elephant random walk in the superdiffusive case with a strong elephant component. Applying the martingale convergence theorem, we prove the Central Limit Theorem and the Law of Iterated Logarithm, where a random drift is subtracted from the process considered. |
| title | Limit theorems for the fluctuation of the dynamic elephant random walk in the superdiffusive case |
| topic | Probability |
| url | https://arxiv.org/abs/2503.13810 |