Precise asymptotics in some strong limit theorems for multidimensionally indexed random variables

DOI10.1016/S0047-259X(03)00050-2zbMath1031.60032OpenAlexW1980935218MaRDI QIDQ1403425

Aurel Spătaru, Allan Gut

Publication date: 1 September 2003

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0047-259x(03)00050-2

zbMATH Keywords

strong lawdomain of attractionstable distributionsmultidimensional indicestail probabilities of sums of independent identically distributed random variableslaw of the itererated logarithm

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Inequalities; stochastic orderings (60E15) Sums of independent random variables; random walks (60G50) Large deviations (60F10)

Related Items (20)

Precise asymptotics in the law of the logarithm for random fields in Hilbert space ⋮ A kind of complete moment convergence for self-normalized sums ⋮ An estimate of the remainder of a limit theorem ⋮ On the strong approximation of the non-overlapping \(k\)-spacings process with application to the moment convergence rates ⋮ Asymptotic property for some series of probability ⋮ Marcinkiewicz-Zygmund type law of large numbers for double arrays of random elements in Banach spaces ⋮ Asymptotic results for hybrids of empirical and partial sums processes ⋮ A kind of complete moment convergence for sums of independent and nonidentically distributed random variables ⋮ Precise asymptotics for complete moment convergence of \(U\)-statistics of i.i.d. random variables ⋮ Precise asymptotes in self-normalized sums of iterated logarithm for multidimensionally indexed random variables ⋮ On the hybrids of \(k\)-spacing empirical and partial sum processes ⋮ Convergence rates of the LIL for random fields in Hilbert spaces ⋮ Asymptotics in the Baum-Katz formula for random fields ⋮ Convergence rates for probabilities of moderate deviations for multidimensionally indexed random variables ⋮ A general pattern of asymptotic behavior of the \(R/S\) statistics for linear processes ⋮ Exact asymptotics in log log laws for random fields ⋮ A general law of complete moment convergence for self-normalized sums ⋮ Uniform bounds in normal approximation under negatively associated random fields ⋮ Precise asymptotics in the law of logarithm under dependence assumptions ⋮ Exact rates in complete moment convergence of self-normalized sums for multidimensionally indexed random variables

Cites Work

• Rate of convergence in the strong law of large numbers for martingales
• Strong laws for independent identically distributed random variables indexed by a sector
• Convergence rates for probabilities of moderate deviations for sums of random variables with multidimensional indices
• A remark on the tail probability of a distribution
• Marcinkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices
• 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.
• A Combinatorial Lemma and Its Application to Probability Theory
• A supplement to the strong law of large numbers
• Convergence Rates in the Law of Large Numbers
• The Probability in the Tail of a Distribution
• 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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