On Wasserstein-1 distance in the central limit theorem for elephant random walk

Xiaohui Ma; Mohamed El Machkouri; Xiequan Fan

doi:10.1063/5.0050312

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arXiv · 2111.10016

On Wasserstein-1 distance in the central limit theorem for elephant random walk

Xiaohui Ma·Mohamed El Machkouri·Xiequan Fan

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Abstract

Recently, the elephant random walk has attracted a lot of attentions. A wide range of literature is available for the asymptotic behavior of the process, such as the central limit theorems, functional limit theorems and the law of iterated logarithm. However, there is not result concerning Wassertein-1 distance for the normal approximations.In this paper, we show that the Wassertein-1 distance in the central limit theorem is totally different when a memory parameter $p$ belongs to one of the three cases $0< p < 1/2,$ $1/2< p<3/4$ and $p=3/4.$

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BibTeX RIS

Xiaohui Ma, Mohamed El Machkouri, Xiequan Fan. 2021-11-19. On Wasserstein-1 distance in the central limit theorem for elephant random walk. https://doi.org/10.1063/5.0050312

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