Precise rates in the law of logarithm for the moment convergence of i.i.d. random variables

DOI10.1016/j.jmaa.2006.02.090zbMath1116.60011OpenAlexW1965564520MaRDI QIDQ860604

Tian-Xiao Pang, Jiang Ye, Zhang, Lixin

Publication date: 9 January 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.02.090

zbMATH Keywords

momentprecise asymptoticsi.i.d. random variablesthe law of logarithm

Mathematics Subject Classification ID

Limit theorems in probability theory (60F99)

Related Items (13)

A general law of moment convergence rates for uniform empirical process ⋮ Convergence rates in the law of large numbers and new kinds of convergence of random variables ⋮ On the precise rates in the law of the logarithm for positively associated sequence ⋮ A note on the Chover-type law of the iterated logarithm for the weighted partial sums of \(\alpha\)-mixing sequences ⋮ Rate of convergence in a theorem of Heyde ⋮ Precise asymptotics in the law of iterated logarithm for the first moment convergence of i.i.d. random variables ⋮ Toeplitz lemma, complete convergence, and complete moment convergence ⋮ Precise asymptotics for the first moment of the error variance estimator in linear models ⋮ Exact rates in the Davis-Gut law of iterated logarithm for the first-moment convergence of independent identically distributed random variables ⋮ Precise rates in the law of the iterated logarithm for the first moment convergence ⋮ The precise asymptotic behavior of parameter estimators in Ornstein-Uhlenbeck process ⋮ Complete moment and integral convergence for sums of negatively associated random variables ⋮ Precise asymptotics in complete moment convergence of the associated counting process

Cites Work

• Some results on convergence rates for probabilities of moderate deviations for sums of random variables
• Limit theorems for delayed sums
• A remark on the tail probability of a distribution
• The Darling-Erdős theorem for sums of i.i.d. random variables
• Precise asymptotics in Spitzer's law of large numbers
• Precise asymptotics in the Baum-Katz and Davis laws of large numbers
• Precise asymptotics in the law of the iterated logarithm.
• The law of the iterated logarithm for identically distributed random variables
• A supplement to the strong law of large numbers
• Some One-Sided Theorems on the Tail Distribution of Sample Sums with Applications to the Last Time and Largest Excess of Boundary Crossings
• Convergence Rates in the 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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