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arXiv · 2109.10301

Reinforced random walks under memory lapses

Manuel González-Navarrete·Ranghely Hernández
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Abstract

We introduce a one-dimensional random walk, which at each step performs a reinforced dynamics with probability $\theta$ and with probability $1 - \theta$, the random walk performs a step independent of the past. We analyse its asymptotic behaviour, showing a law of large numbers and characterizing the diffusive and superdiffusive regions. We prove central limit theorems and law of iterated logarithm based on the martingale approach.

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Manuel González-Navarrete, Ranghely Hernández. 2021-09-21. Reinforced random walks under memory lapses. https://doi.org/10.1007/s10955-021-02826-x

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