Finite-memory elephant random walk and the central limit theorem for additive functionals

DOI10.1214/20-BJPS475zbMath1471.60108arXiv1911.05716OpenAlexW3154748779MaRDI QIDQ2233657

Xioran Tan, Jonah Green, Hugo Panzo, Taylor Meredith, Iddo Ben-Ari

Publication date: 11 October 2021

Published in: Brazilian Journal of Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.05716

zbMATH Keywords

central limit theoremadditive functionalfinite-state Markov chainelephant random walk

Mathematics Subject Classification ID

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

Related Items (2)

The elephant random walk with gradually increasing memory ⋮ Limit theorems for a random walk with memory perturbed by a dynamical system

Cites Work

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• Markov chains and stochastic stability
• Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions
• Central limit theorems for additive functionals of Markov chains.
• Central limit theorem started at a point for stationary processes and additive functionals of reversible Markov chains
• A martingale approach for the elephant random walk
• Central limit theorem and related results for the elephant random walk
• Matrix Iterative Analysis
• Probability: A Graduate Course

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