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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

A strong invariance principle for the elephant random walk

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Author(s):
Coletti, Cristian F. [1] ; Gava, Renato [2] ; Schutz, Gunter M. [3]
Total Authors: 3
Affiliation:
[1] UFABC, Ctr Matemat Comp & Cognicao, Ave Estados 5001, Sao Paulo - Brazil
[2] Univ Fed Sao Carlos, Dept Estat, Rodovia Washington Luiz, Km 235, BR-13565905 Sao Carlos - Brazil
[3] Forschungszentrum Julich, Inst Complex Syst 2, D-52425 Julich - Germany
Total Affiliations: 3
Document type: Journal article
Source: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT; DEC 2017.
Web of Science Citations: 6
Abstract

We consider a non-Markovian discrete-time random walk on Z with unbounded memory, called the elephant random walk (ERW). We prove a strong invariance principle for the ERW. More specifically, we prove that, under a suitable scaling and in the diffusive regime as well as at the critical value p(c) = 3/4 where the model is marginally superdiffusive, the ERW is almost surely well approximated by a Brownian motion. As a by-product of our result we get the law of iterated logarithm and the central limit theorem for the ERW. (AU)

FAPESP's process: 16/11648-0 - Limit theorems and phase transition results for information propagation models on graphs
Grantee:Pablo Martin Rodriguez
Support Opportunities: Regular Research Grants
FAPESP's process: 15/20110-0 - Branching Random Walks and Interacting particle System in Random Environment.
Grantee:Cristian Favio Coletti
Support Opportunities: Scholarships abroad - Research