Multidimensional walks with random tendency

Abstract

We introduce a multidimensional walk with memory and random tendency. The asymptotic behaviour is characterized, proving a law of large numbers and showing a phase transition from diffusive to superdiffusive regimes. In first case, we obtain a functional limit theorem to Gaussian vectors. In superdiffusive, we obtain strong convergence to a non-Gaussian random vector and characterize its moments.

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Cited by in corpus (3)

• On the elephant random walk with stops playing hide and seek with the Mittag-Leffler distribution
• Joint invariance principles for random walks with positively and negatively reinforced steps
• Reinforced random walks under memory lapses