Gaussian fluctuations of the elephant random walk with gradually increasing memory

DOI10.1088/1751-8121/ad1c0dOpenAlexW4390658421MaRDI QIDQ6121756

Mohamed El Machkouri, Rafik Aguech

Publication date: 27 February 2024

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1751-8121/ad1c0d

zbMATH Keywords

asymptotic normalityphase transitioncentral limit theoremmartingale theoryLindeberg's methodelephant random walk

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50)

Cites Work

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• Introducing smooth amnesia to the memory of the elephant random walk
• The elephant random walk with gradually increasing memory
• On the elephant random walk with stops playing hide and seek with the Mittag-Leffler distribution
• Gaussian fluctuation for superdiffusive elephant random walks
• On the multi-dimensional elephant random walk
• A martingale approach for the elephant random walk
• On Wasserstein-1 distance in the central limit theorem for elephant random walk
• Variations of the elephant random walk
• Central limit theorem and related results for the elephant random walk
• Rates of convergence in the central limit theorem for the elephant random walk with random step sizes

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