On the limit behaviour of weighted sums of random variables

DOI10.1007/BF00532224zbMath0482.60023MaRDI QIDQ3940557

Hall, Peter, Harry Cohn

Publication date: 1982

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

zbMATH Keywords

stable lawsrates of convergenceweighted sums

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50)

Related Items (4)

Convergence in probability and almost sure with applications. ⋮ Asymptotics for ratios with applications to reinsurance ⋮ Weak laws of large numbers for cooperative gamblers ⋮ Norming constants for the finite mean supercritical Bellman-Harris process

Cites Work

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• Limit theorems for weighted sums of random elements in separable Banach spaces
• The expected ratio of the sum of squares to the square of the sum
• Note on a limit theorem
• A strong law for weighted averages of independent, identically distributed random variables with arbitrarily heavy tails
• Convergence to zero of quadratic forms in independent random variables
• Limit distributions of self-normalized sums
• On the elementary renewal theorem for non-identically distributed variables
• On one-sided boundedness of normed partial sums
• Norming constants for the finite mean supercritical Bellman-Harris process
• On the L^p convergence of sums of independent random variables
• Convergence of weighted averages of independent random variables
• Almost Certain Summability of Independent, Identically Distributed Random Variables
• Variations on a Renewal Theorem of Smith
• The Erdos-Renyi New Law of Large Numbers for Weighted Sums

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