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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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On the Strong Law of Large Numbers [PDF]
Proceedings of the American Mathematical Society, 1970 indicator variables given by F*(X) = 1 if | Sk — kp\ =\k, and 0 otherwise, and let JV»(X) = z2? ^(X)- Then ATM(X) = Jji" Yk(\) is precisely the "finitely many" random variable of the Strong Law of Large Numbers. Indeed, this law may be formulated in terms of this counting variable as in the following. Strong law of large numbers.
Slivka, J., Severo, N. C.
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On the Strong Law of Large Numbers [PDF]
Transactions of the American Mathematical Society, 1949 \(f(x) = f(x+1)\) besitze in \((0,1)\) den Mittelwert Null sowie die Streuung Eins und \((n_k)\) sei eine Folge von natürlichen Zahlen mit \(n_{k+1}/n_k > c > 1\). Die Frage, welche Bedingung das sog. starke Gesetz \[ g = \lim_{N\to \infty} \sum_{k=1}^N f(n_k x)/N = 0 \] für fast alle \(x\) sichert, ist von Kac, Salem, Zygmund unlängst mit den \(n ...
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A strong law of large numbers for capacities [PDF]
The Annals of Probability, 2005 We consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables. We show that, on a full set, any cluster point of empirical averages lies between the lower and the upper Choquet integrals of the random variables, provided either the random variables or the capacity are continuous.
Maccheroni, Fabio, Marinacci, Massimo
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An extension of Feller’s strong law of large numbers [PDF]
Statistics & Probability Letters, 2018 10 pages. arXiv admin note: text overlap with arXiv:1703.07868.
Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, Canada ( host institution ) +3 more
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International Journal of Mathematics and Mathematical Sciences, 1999 Let {Xij} be a double sequence of pairwise independent random variables.
Dug Hun Hong, Seok Yoon Hwang
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Strong laws of large numbers for general random variables in sublinear expectation spaces
Journal of Inequalities and Applications, 2019 In this paper, we obtain the equivalent relations between Kolmogorov maximal inequality and Hájek–Rényi maximal inequality both in moment and capacity types in sublinear expectation spaces.
Weihuan Huang, Panyu Wu
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Further Spitzer’s law for widely orthant dependent random variables
Journal of Inequalities and Applications, 2021 The Spitzer’s law is obtained for the maximum partial sums of widely orthant dependent random variables under more optimal moment conditions.
Pingyan Chen, Jingjing Luo, Soo Hak Sung
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On conditions for the strong law of large numbers in general Banach spaces
International Journal of Mathematics and Mathematical Sciences, 2000 We give Chung-Teicher type conditions for the SLLN in general Banach spaces under the assumption that the weak law of large numbers holds. An example is provided showing that these conditions can hold when some earlier known conditions fail.
Anna Kuczmaszewska, Dominik Szynal
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Strong Law of Large Numbers of Pettis-Integrable Multifunctions
Journal of Mathematics, 2019 Using reversed martingale techniques, we prove the strong law of large numbres for independent Pettis-integrable multifunctions with convex weakly compact values in a Banach space.
Hamid Oulghazi, Fatima Ezzaki
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