The elephant random walk with gradually increasing memory

DOI10.1016/j.spl.2022.109598zbMath1496.60020arXiv2110.13497OpenAlexW3210703628MaRDI QIDQ2170249

Allan Gut, Ulrich Stadtmüller

Publication date: 30 August 2022

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.13497

zbMATH Keywords

momentsdelaycentral limit theoremelephant random walkgradually increasing memory

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

Related Items (3)

Analysis of the smoothly amnesia-reinforced multidimensional elephant random walk ⋮ Gaussian fluctuations of the elephant random walk with gradually increasing memory ⋮ Introducing smooth amnesia to the memory of the elephant random walk

Cites Work

• Limit theorems for correlated Bernoulli random variables
• Transient superdiffusion in random walks with a \(q\)-exponentially decaying memory profile
• Finite-memory elephant random walk and the central limit theorem for additive functionals
• The number of zeros in elephant random walks with delays
• Hypergeometric identities arising from the elephant random walk
• Amnestically Induced Persistence in Random Walks
• A martingale approach for the elephant random walk
• Asymptotics and Criticality for a Correlated Bernoulli Process
• Variations of the elephant random walk
• Central limit theorem and related results for the elephant random walk

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