Convergence and precise asymptotics for series involving self-normalized sums

DOI10.1007/S10959-014-0560-1zbMath1335.60052OpenAlexW2003597301MaRDI QIDQ270217

Aurel Spătaru

Publication date: 7 April 2016

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10959-014-0560-1

zbMATH Keywords

asymptoticsdomain of attractionstable lawself-normalized sums

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Limit theorems in probability theory (60F99)

Related Items (2)

Precise asymptotics of weighted sequences and their applications ⋮ General results on precise asymptotics under sub-linear expectations

Cites Work

• Precise asymptotics in Spitzer's law of large numbers
• When is the Student \(t\)-statistic asymptotically standard normal?
• An exponential nonuniform Berry-Esseen bound for self-normalized sums
• Precise asymptotics in the Baum-Katz and Davis laws of large numbers
• Limit distributions of self-normalized sums
• Strengthening classical results on convergence rates in strong limit theorems
• GENERAL LAWS OF PRECISE ASYMPTOTICS FOR SUMS OF RANDOM VARIABLES
• A supplement to the strong law of large numbers
• Complete Convergence and the Law of Large Numbers
• On a Theorem of Hsu and Robbins
• Remark on my Paper "On a Theorem of Hsu and Robbins"

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