Cramér moderate deviations for the elephant random walk

DOI10.1088/1742-5468/abd942OpenAlexW3126721850MaRDI QIDQ5857518

Xiequan Fan, Xiaohui Ma, Haijuan Hu

Publication date: 1 April 2021

Published in: Journal of Statistical Mechanics: Theory and Experiment (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.12937

zbMATH Keywords

stochastic processeslarge deviation

Mathematics Subject Classification ID

Statistical mechanics, structure of matter (82-XX)

Related Items (8)

Limiting behaviors of generalized elephant random walks ⋮ On Wasserstein-1 distance in the central limit theorem for elephant random walk ⋮ On the elephant random walk with stops playing hide and seek with the Mittag-Leffler distribution ⋮ Rates of convergence in the central limit theorem for the elephant random walk with random step sizes ⋮ Analysis of the smoothly amnesia-reinforced multidimensional elephant random walk ⋮ Sharp moderate and large deviations for sample quantiles ⋮ New insights on the reinforced elephant random walk using a martingale approach ⋮ Rate of moment convergence in the central limit theorem for the elephant random walk

Cites Work

• Large deviations for martingales via Cramér's method
• Exact rates of convergence in some martingale central limit theorems
• Cramér moderate deviation expansion for martingales with one-sided Sakhanenko's condition and its applications
• On the multi-dimensional elephant random walk
• Exact convergence rates in the central limit theorem for a class of martingales
• A strong invariance principle for the elephant random walk
• A martingale approach for the elephant random walk
• Central limit theorem and related results for the elephant random walk
• On the almost sure central limit theorem for the elephant random walk

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