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The elephant random walk in the triangular array setting

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arxiv 2403.02881 v1 pith:OEB4GV5Y submitted 2024-03-05 math.PR

Rahul Roy , Masato Takei , Hideki Tanemura This is my paper · ORCID
classification math.PR
keywords elephantllerrandomwalkstadtmarraydefinitionmemory
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Gut and Stadm\"{u}ller (2021, 2022) initiated the study of the elephant random walk with limited memory. Aguech and El Machkouri (2024) published a paper in which they discuss an extension of results by Gut and Stadtm\"{u}ller (2022) for an "increasing memory" version of the elephant random walk without stops. Here we present a formal definition of the process which has been hinted at Eq. (2.2) in Gut and Stadtm\"{u}ller (2022). This definition is based on the triangular array setting. We give a positive answer to the open problem in Gut and Stadtm\"{u}ller (2022) for the elephant random walk, possibly with stops. We also obtain the CLT for the supercritical case of this model.

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