A universal scaling limit for diffusive amnesic step-reinforced random walks
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913234493112320 |
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| author | Bertenghi, Marco Laulin, Lucile |
| author_facet | Bertenghi, Marco Laulin, Lucile |
| contents | We introduce a variation of the step-reinforced random walk with general memory. For the diffusive regime, we establish a functional invariance principle and show that, given suitable conditions on the memory sequence, the arising limiting processes are always the sum of a noise reinforced Brownian motion and a (not independent) Brownian motion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09202 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A universal scaling limit for diffusive amnesic step-reinforced random walks Bertenghi, Marco Laulin, Lucile Probability We introduce a variation of the step-reinforced random walk with general memory. For the diffusive regime, we establish a functional invariance principle and show that, given suitable conditions on the memory sequence, the arising limiting processes are always the sum of a noise reinforced Brownian motion and a (not independent) Brownian motion. |
| title | A universal scaling limit for diffusive amnesic step-reinforced random walks |
| topic | Probability |
| url | https://arxiv.org/abs/2402.09202 |