An infinite-dimensional law of large numbers in Cesaro's sense

DOI10.1007/BF01046094zbMath0707.60011WikidataQ112879217 ScholiaQ112879217MaRDI QIDQ919698

Bernard Heinkel

Publication date: 1990

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

zbMATH Keywords

strong law of large numbersexponential inequalitiesCesaro summability

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (9)

Complete convergence and Cesàro summation for i.i.d. random variables ⋮ Complete convergence and almost sure convergence of weighted sums of random variables ⋮ A note on moments of the maximum of Cesàro summation ⋮ Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of random variables with infinite moment and its applications ⋮ Cesàro summation for random fields ⋮ A Marcinkiewicz-Zygmund type strong law for weighted sums of \(\phi \)-mixing random variables and its applications ⋮ Strong limit theorems for weighted sums of negatively associated random variables ⋮ Weighted strong laws of large numbers on variable exponent vector-valued Lebesgue spaces ⋮ On Valiron means of \(B\)-valued random variables

Cites Work

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• On the almost sure convergence, of order \(\alpha\) in the sense of Césaro, \(0<\alpha<1\), for independent and identically distributed random variables.
• Stabilité de sommes pondérées de variables aléatoires vectorielles. (Stability of weighted sums of vector random variables)
• Inequalities for B-valued random vectors with applications to the strong law of large numbers
• Limiting behavior of weighted sums of independent random variables
• Some stability results for vector valued random variables
• Borel and Banach properties of methods of summation
• Tail probabilities for sums of independent Banach space valued random variables
• Sums of independent Banach space valued random variables

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