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On the center of mass of the elephant random walk
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BERCU, Bernard | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | LAULIN, Lucile | |
| dc.date.accessioned | 2024-04-04T02:37:04Z | |
| dc.date.available | 2024-04-04T02:37:04Z | |
| dc.date.issued | 2021-03 | |
| dc.identifier.issn | 0304-4149 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190773 | |
| dc.description.abstractEn | Our goal is to investigate the asymptotic behavior of the center of mass of the elephant random walk, which is a discrete-time random walk on integers with a complete memory of its whole history. In the diffusive and critical regimes, we establish the almost sure convergence, the law of iterated logarithm and the quadratric strong law for the center of mass of the elephant random walk. The asymptotic normality of the center of mass, properly normalized, is also provided. Finally, we prove a strong limit theorem for the center of mass in the superdiffusive regime. All our analysis relies on asymptotic results for multi-dimensional martingales. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc/ | |
| dc.title.en | On the center of mass of the elephant random walk | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.spa.2020.11.004 | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.identifier.arxiv | 1911.06781 | |
| bordeaux.journal | Stochastic Processes and their Applications | |
| bordeaux.page | 111-128 | |
| bordeaux.volume | 133 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02495895 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02495895v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Stochastic%20Processes%20and%20their%20Applications&rft.date=2021-03&rft.volume=133&rft.spage=111-128&rft.epage=111-128&rft.eissn=0304-4149&rft.issn=0304-4149&rft.au=BERCU,%20Bernard&LAULIN,%20Lucile&rft.genre=article |
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