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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.)

Limit theorems for a minimal random walk model

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Author(s):
Coletti, Cristian F. [1] ; Gava, Renato J. [2] ; de Lima, Lucas R. [1]
Total Authors: 3
Affiliation:
[1] UFABC Ctr Matemat Comp & Cognicao, Ave Estados 5001, Santo Andre, SP - Brazil
[2] UFSCAR Dept Estat, Rodovia Washington Luiz, Km 235, BR-13565905 Sao Carlos, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT; AUG 2019.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 17/10555-0 - Stochastic modeling of interacting systems
Grantee:Fabio Prates Machado
Support type: Research Projects - Thematic Grants
FAPESP's process: 18/04764-9 - Random walks with unbounded memory
Grantee:Renato Jacob Gava
Support type: Scholarships abroad - Research