On the asymptotics of a lazy reinforced random walk
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866917588781498368 |
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| author | González-Navarrete, Manuel Lambert, Rodrigo Guevara, Víctor Hugo Vázquez |
| author_facet | González-Navarrete, Manuel Lambert, Rodrigo Guevara, Víctor Hugo Vázquez |
| contents | Based on a martingale theory approach, we present a complete characterization of the asymptotic behaviour of a lazy reinforced random walk (LRRW) which shows three different regimes (diffusive, critical and superdiffusive). This allows us to prove versions of the law of large numbers, the quadratic strong law, the law of iterated logarithm, the almost sure central limit theorem and the functional central limit theorem in the diffusive and critical regimes. In the superdiffusive regime we obtain a strong convergence to a random variable, including a central limit theorem and a law of iterated logarithm for the fluctuations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08033 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the asymptotics of a lazy reinforced random walk González-Navarrete, Manuel Lambert, Rodrigo Guevara, Víctor Hugo Vázquez Probability G.3 Based on a martingale theory approach, we present a complete characterization of the asymptotic behaviour of a lazy reinforced random walk (LRRW) which shows three different regimes (diffusive, critical and superdiffusive). This allows us to prove versions of the law of large numbers, the quadratic strong law, the law of iterated logarithm, the almost sure central limit theorem and the functional central limit theorem in the diffusive and critical regimes. In the superdiffusive regime we obtain a strong convergence to a random variable, including a central limit theorem and a law of iterated logarithm for the fluctuations. |
| title | On the asymptotics of a lazy reinforced random walk |
| topic | Probability G.3 |
| url | https://arxiv.org/abs/2402.08033 |