Non-Markovian random walks with memory lapses
| Autor: | González-Navarrete, Manuel, Lambert, Rodrigo |
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| Rok vydání: | 2016 |
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| Druh dokumentu: | Working Paper |
| Popis: | We propose an approach to construct Bernoulli trials $\{X_i, i\ge 1\}$ combining dependence and independence periods, and call it Bernoulli sequence with random dependence (BSRD). The structure of dependence, on the past $S_i = X_1 + \ldots + X_i$, {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 $\{Y_i, i\ge 1\}$, called {\it memory switch sequence}. We introduce the concept of {\it memory lapses 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 literature. Along the paper, several examples of potential applications are provided. Comment: 14 pages |
| Databáze: | arXiv |
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