Limit theorems for a minimal random walk model

Autor(es)

Coletti, Cristian F. ; Gava, Renato J. ; de Lima, Lucas R.

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT; v. N/A, p. 13-pg., 2019-08-01.

Resumo

We study the minimal random walk introduced by Kumar et al (2014 Phys. Rev. E 90 022136). It is a random process on {0,1, ...} with unbounded memory which exhibits subdiffusive, diffusive and superdiffusive regimes. We prove the law of large numbers for the whole parameter set. Then we prove the central limit theorem and the law of the iterated logarithm for the minimal random walk under diffusive and marginally superdiffusive behaviors. More interestingly, we establish a result for the minimal random walk when it possesses the three regimes; we show the convergence of its resealed version to a non-normal random variable. (AU)

• Processo FAPESP: 17/10555-0 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Fabio Prates Machado
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 18/04764-9 - Passeios aleatórios com memória ilimitada
• Beneficiário: Renato Jacob Gava
• Modalidade de apoio: Bolsas no Exterior - Pesquisa