Limit Properties of Record Numbers in Random walks
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914655782305792 |
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| author | Lu, Penghui Li, Yuqiang Yao, Qiang |
| author_facet | Lu, Penghui Li, Yuqiang Yao, Qiang |
| contents | In this paper, we systematically summarize and enhance the understanding of weak convergence and functional limits of record numbers in discrete-time random walks under Spitzer's condition, and extend these findings to $σ$--record numbers using similar methods. Additionally, we identify a sufficient condition for the existence of functional limits for record numbers in continuous-time random walks. Finally, we derive corresponding results for large deviations, moderate deviations, and laws of the iterated logarithm pertaining to record numbers in discrete-time random walks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15445 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limit Properties of Record Numbers in Random walks Lu, Penghui Li, Yuqiang Yao, Qiang Probability In this paper, we systematically summarize and enhance the understanding of weak convergence and functional limits of record numbers in discrete-time random walks under Spitzer's condition, and extend these findings to $σ$--record numbers using similar methods. Additionally, we identify a sufficient condition for the existence of functional limits for record numbers in continuous-time random walks. Finally, we derive corresponding results for large deviations, moderate deviations, and laws of the iterated logarithm pertaining to record numbers in discrete-time random walks. |
| title | Limit Properties of Record Numbers in Random walks |
| topic | Probability |
| url | https://arxiv.org/abs/2401.15445 |