Central limit theorem and related results for the elephant random walk

Autor(es)

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

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Physics; v. 58, n. 5 MAY 2017.
• Citações Web of Science: 14

Resumo

We study the so-called elephant random walk (ERW) which is a non-Markovian discrete-time random walk on Z with unbounded memory which exhibits a phase transition from a diffusive to superdiffusive behavior. We prove a law of large numbers and a central limit theorem. Remarkably the central limit theorem applies not only to the diffusive regime but also to the phase transition point which is superdiffusive. Inside the superdiffusive regime, the ERW converges to a non-degenerate random variable which is not normal. We also obtain explicit expressions for the correlations of increments of the ERW. Published by AIP Publishing. (AU)

• Processo FAPESP: 15/20110-0 - Passeios Aleatórios com Ramificação e Sistemas de Partículas em Ambiente Aleatório.
• Beneficiário: Cristian Favio Coletti
• Modalidade de apoio: Bolsas no Exterior - Pesquisa