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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.)

Non-Markovian random walks with memory lapses

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Gonzalez-Navarrete, Manuel [1] ; Lambert, Rodrigo [2, 3]
Total Authors: 2
[1] Univ Bio Bio, Dept Estadist, Concepcion - Chile
[2] Univ Fed Uberlandia, Fac Matemat, Salvador, BA - Brazil
[3] Univ Fed Bahia, Dept Matemat, Salvador, BA - Brazil
Total Affiliations: 3
Document type: Journal article
Source: Journal of Mathematical Physics; v. 59, n. 11 NOV 2018.
Web of Science Citations: 0

We propose an approach to construct Bernoulli trials [X-i, i >= 1] combining dependence and independence periods, and we call it the Bernoulli sequence with random dependence (BSRD). The structure of dependence, in the past S-i = X-1 + ... + X-i, defines a class of non-Markovian random walks of recent interest in the literature. In this paper, the dependence is activated by an auxiliary collection of Bernoulli trials [Y-i, i >= 1], called memory switch sequence. We introduce the concept of memory lapse property, which is characterized by intervals of consecutive independent steps in BSRD. The main results include classical limit theorems for a class of linear BSRD. In particular, we obtain a central limit theorem for a class of BSRD which generalizes some previous results in the literature. Along the paper, several examples of potential applications are provided. Published by AIP Publishing. (AU)

FAPESP's process: 14/19805-1 - Statistics of extreme events and dynamics of recurrence
Grantee:Miguel Natalio Abadi
Support Opportunities: Regular Research Grants
FAPESP's process: 15/02801-6 - Ising models with periodical external fields: phase diagrams and stochastic evolution
Grantee:Manuel Alejandro González Navarrete
Support Opportunities: Scholarships in Brazil - Post-Doctorate