Non-Gaussian behavior of reflected fractional Brownian motion

Autor(es)

Wada, Alexander H. O. ^{[1, 2]} ; Warhover, Alex ^[1] ; Vojta, Thomas ^[1]

Afiliação do(s) autor(es)

^[1] Missouri Univ Sci & Technol, Dept Phys, Rolla, MO 65409 - USA

^[2] Univ Sao Paulo, Inst Fis, Rua Matao 1371, BR-05508090 Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT; MAR 2019.
• Citações Web of Science: 1

Resumo

A possible mechanism leading to anomalous diffusion is the presence of long-range correlations in time between the displacements of the particles. Fractional Brownian motion, a non-Markovian self-similar Gaussian process with stationary increments, is a prototypical model for this situation. Here, we extend the previous results found for unbiased reflected fractional Brownian motion (Wada et al 2018 Phys. Rev. E 97 020102) to the biased case by means of Monte Carlo simulations and scaling arguments. We demonstrate that the interplay between the reflecting wall and the correlations leads to highly non-Gaussian probability densities of the particle position x close to the reflecting wall. Specifically, the probability density P(x) develops a power-law singularity P similar to x(kappa) with kappa < 0 if the correlations are positive (persistent) and kappa > 0 if the correlations are negative (antipersistent). We also analyze the behavior of the large-x tail of the stationary probability density reached for bias towards the wall, the average displacements of the walker, and the first-passage time, i.e. the time it takes for the walker reach position x for the first time. (AU)

• Processo FAPESP: 17/08631-0 - Transições de fase fora do equilíbrio na presença de desordem temporal
• Beneficiário: Alexander Hideki Oniwa Wada
• Linha de fomento: Bolsas no Exterior - Estágio de Pesquisa - Doutorado