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ON THE STRONG LAW OF LARGE NUMBERS.
ON THE STRONG LAW OF LARGE NUMBERS.This note examines the connection between general moment conditions and the applicability of the strong law of large numbers to a sequence of identically distributed random variables. Some generalizations of the Marcinkiewicz-Zygmund theorem are obtained.
Petrov, Valentin V.
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Uniform Strong Law of Large Numbers [PDF]
Methodology and Computing in Applied Probability, 2019 The authors consider random signed measures \(\xi\) on \(\mathbb R^d\) and show that some strong law of large for \(\xi\) already implies that this law holds uniformly over all Borel sets whenever \(\xi\) is dominated by some positive random measure with the same limit behavior (and under some additional technical condition). The authors also show that
V. Yu. Bogdanskii +2 more
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Bernoulli's Law of Large Numbers and the Strong Law of Large Numbers
Theory of Probability and Its Applications, 2016We discuss the connection between the law of large numbers and the strong law of large number for sums of independent random variables. The mathematical content of these laws and their connection with mathematical statistics problems is compared.
D M Chibisov
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ON THE STRONG LAW OF LARGE NUMBERS
Acta Mathematica Scientia, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qiu, Dehua, Gan, Shixin
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A Note on the Strong Law of Large Numbers
Calcutta Statistical Association Bulletin, 1994Let { X n } be a sequence of pairwise independent (or -mixing) mean zero random variables such that [Formula: see text] is integrable on (0,ā) and [Formula: see text] then we show that [Formula: see text] almost surely as nāā, These are very convenient and immediate generalizations of the ...
Bose, Arup, Chandra, Tapas K.
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On the strong law of large numbers
Statistics & Probability Letters, 1969The connection between general moment conditions and SLLN for identically distributed random variables is examined. Let \(f(x)\) be an positive even continuous function strictly increasing in the region \(x>0\) and \(f(+\infty)=\infty\), \(a_n=f^{-1}(n)\) where \(f^{-1}\) is the inverse of \(f\). The following two statements are proved. 1) Let \(\{X_n\}
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The Strong Law of Large Numbers
1991In this chapter and in the next one, we present respectively the strong law of large numbers and the law of the iterated logarithm for sums of independent Banach space valued random variables. In this study, the isoperimetric approach of Section 6.3 demonstrates its efficiency. We only investigate extensions to vector valued random variables of some of
Michel Ledoux, Michel Talagrand
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