Finite-Memory Elephant Random Walk and the Central Limit Theorem for Additive Functionals

Iddo Ben-Ari; Jonah Green; Taylor Meredith; Hugo Panzo; Xiaoran Tan

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arXiv · 1911.05716

Finite-Memory Elephant Random Walk and the Central Limit Theorem for Additive Functionals

Iddo Ben-Ari·Jonah Green·Taylor Meredith·Hugo Panzo·Xiaoran Tan

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Abstract

The Central Limit Theorem (CLT) for additive functionals of Markov chains is a well known result with a long history. In this paper we present applications to two finite-memory versions of the Elephant Random Walk, solving a problem from arXiv:1812.01915. We also present a derivation of the CLT for additive functionals of finite state Markov chains, which is based on positive recurrence, the CLT for IID sequences and some elementary linear algebra, and which focuses on characterization of the variance.

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Iddo Ben-Ari, Jonah Green, Taylor Meredith, Hugo Panzo, Xiaoran Tan. 2019-11-13. Finite-Memory Elephant Random Walk and the Central Limit Theorem for Additive Functionals. https://arxiv.org/abs/1911.05716

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