The central limit theorem for summability methods of I.I.D. random variables

DOI10.1007/BF00531777zbMath0535.60018OpenAlexW1990588956MaRDI QIDQ3319483

Makoto Maejima, Paul Embrechts

Publication date: 1984

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00531777

zbMATH Keywords

rate of convergencecentral limit theoremsummability methods

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Special methods of summability (40Gxx)

Related Items (18)

Stochastic random walk summability ⋮ Central limit theorems for sub-linear expectation under the Lindeberg condition ⋮ The central limit theorem for summability methods of some weakly dependent sequences ⋮ Riesz and Valiron means and fractional moments ⋮ On The Properties Of Random Entire Functions ⋮ Limit theorems for methods of summation of independent random variables. I ⋮ Limit theorems for the discount sums of moving averages ⋮ Non-uniform rates of convergence for double arrays of independent random variables with applications ⋮ Asymptotic normality in Banach spaces via Lindeberg method ⋮ A Conversation With Paul Embrechts ⋮ The chover-type law of iterated logarithm for the weighted sums of negatively superadditive dependent random variables ⋮ On complete convergence and strong law for weighted sums of i.i.d. random variables ⋮ The law of the iterated logarithm for certain power series and generalized Nörlund methods ⋮ A quantitative discounted central limit theorem using the Fourier metric ⋮ Summability methods and almost sure convergence ⋮ Asymptotic normality of sums of Hilbert space valued random elements ⋮ Weighted sums of random variables attracted to stable laws ⋮ Functional limit theorems for weighted sums of i.i.d. random variables

Cites Work

• Tauberian theorems and the central limit theorem
• A nonuniform bound on convergence to normality
• Summability Methods for Independent, Identically Distributed Random Variables
• Refinement of Lindeberg’s Theorem
• The Discounted Central Limit Theorem and its Berry-Esseen Analogue
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The central limit theorem for summability methods of I.I.D. random variables