Sub-diffusive behavior of a recurrent Axis-Driven Random Walk
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910905394003968 |
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| author | Andreoletti, Pierre Debs, Pierre |
| author_facet | Andreoletti, Pierre Debs, Pierre |
| contents | We study the second order of the number of excursions of a simple random walk with a bias that drives a return toward the origin along the axes introduced by P. Andreoletti and P. Debs \cite{AndDeb3}. This is a crucial step toward deriving the asymptotic behavior of these walks, whose limit is explicit and reveals various characteristics of the process: the invariant probability measure of the extracted coordinates away from the axes, the 1-stable distribution arising from the tail distribution of entry times on the axes, and finally, the presence of a Bessel process of dimension 3, which implies that the trajectory can be interpreted as a random path conditioned to stay within a single quadrant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04972 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sub-diffusive behavior of a recurrent Axis-Driven Random Walk Andreoletti, Pierre Debs, Pierre Probability We study the second order of the number of excursions of a simple random walk with a bias that drives a return toward the origin along the axes introduced by P. Andreoletti and P. Debs \cite{AndDeb3}. This is a crucial step toward deriving the asymptotic behavior of these walks, whose limit is explicit and reveals various characteristics of the process: the invariant probability measure of the extracted coordinates away from the axes, the 1-stable distribution arising from the tail distribution of entry times on the axes, and finally, the presence of a Bessel process of dimension 3, which implies that the trajectory can be interpreted as a random path conditioned to stay within a single quadrant. |
| title | Sub-diffusive behavior of a recurrent Axis-Driven Random Walk |
| topic | Probability |
| url | https://arxiv.org/abs/2504.04972 |