Large deviations for martingales with some applications

DOI10.1007/BF00992617zbMath0826.60021MaRDI QIDQ1897265

Alfredas Račkauskas

Publication date: 14 November 1995

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

zbMATH Keywords

central limit theoremlarge deviationsrate of uniform convergencemartingale difference sequence

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05) Large deviations (60F10)

Related Items

Non-uniform Berry–Esseen bounds for martingales with applications to statistical estimation ⋮ Large deviations for martingales via Cramér's method ⋮ Cramér moderate deviation expansion for martingales with one-sided Sakhanenko's condition and its applications ⋮ Self-normalized Cramér type moderate deviations for stationary sequences and applications ⋮ Moderate deviation principle for Brownian motions on the unit sphere in \(\mathbb R^d\) ⋮ A generalization of Cramér large deviations for martingales ⋮ Cramér-type moderate deviations for stationary sequences of bounded random variables ⋮ Cramér type moderate deviations for self-normalized \(\psi \)-mixing sequences ⋮ Moderate deviations for martingale differences and applications to φ -mixing sequences

Cites Work

• On the rate of convergence in the central limit theorem for martingales with discrete and continuous time
• A nonuniform bound on the rate of convergence in the martingale central limit theorem
• On probabilities of large deviations in Banach spaces
• Exact convergence rates in some martingale central limit theorems
• Best constants in martingale version of Rosenthal's inequality
• Certain non-uniform rates of convergence to normality for a restricted class of martingales
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