Reinforced random walks under memory lapses

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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Cited by in corpus (1)

• On the elephant random walk with stops playing hide and seek with the Mittag-Leffler distribution