A strong invariance principle for the elephant random walk

Autor(es)

Coletti, Cristian F. ; Gava, Renato ; Schutz, Gunter M.

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT; v. N/A, p. 8-pg., 2017-12-01.

Resumo

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)

• Processo FAPESP: 15/20110-0 - Passeios Aleatórios com Ramificação e Sistemas de Partículas em Ambiente Aleatório.
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