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A note on the strong law of large numbers
, 1968 identically distributed (i.i.d.) random variables. Let Sn-t^Xk (fl » 1, 2, • • •)• J f e- 1 A long standing problem in probability theory has been to find ...
Katz, M. +3 more
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A Note on Chung's Strong Law of Large Numbers
, 1998 In this paper we generalize the classical Chung's strong law of large numbers. We also prove some results about almost sureA-summability for sequences of independent random variables, whereAis a suitable real infinite ...
Pečarić, Josip +2 more
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A generalization of the Petrov strong law of large numbers [PDF]
Statistics & Probability Letters, 2015 In 1969 V.V.~Petrov found a new sufficient condition for the applicability of the strong law of large numbers to sequences of independent random variables. He proved the following theorem: let $\{X_{n}\}_{n=1}^{\infty}$ be a sequence of independent random variables with finite variances and let $S_{n}=\sum_{k=1}^{n} X_{k}$. If $Var (S_{n})=O (n^{2}/ψ(n)
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A Note on Feller's Strong Law of Large Numbers
The Annals of Probability, 1986 Let \((X_ n)\) be a sequence of i.i.d. random variables with \(S_ n=\sum^{n}_{j=1}X_ j\), \(n\geq 1\) and let \((\gamma_ n)\) be a sequence of positive constants such that \(\gamma_ n/n\) is not decreasing in n. Define \(\gamma(x)=0\) if \(x=0\), \(=\gamma_ n\) if \(x=n\), \(n\geq 1\) and \(=\gamma_ n+(\gamma_{n+1}-\gamma_ n)(x-n)\) if \(n\leq x\leq n ...
Chow, Yuan Shih, Zhang, Cun-Hui
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Quantitative Strong Laws of Large Numbers
Electronic Journal of ProbabilityUsing proof-theoretic methods in the style of proof mining, we give novel computationally effective limit theorems for the convergence of the Cesaro-means of certain sequences of random variables. These results are intimately related to various Strong Laws of Large Numbers and, in that way, allow for the extraction of quantitative versions of many of ...
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On the Strong Law of Large Numbers in Banach Spaces [PDF]
Proceedings of the American Mathematical Society, 1987 We study the relationship between the geometry of a real separable Banach space B B (as manifested in its cotype, type, or ...
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General Bahr-Esseen inequalities and their applications
Journal of Inequalities and Applications, 2017 We study the Bahr-Esseen inequality. We show that the Bahr-Esseen inequality holds with exponent p if it holds with exponent q > p $q>p$ for the truncated and centered random variables.
István Fazekas, Sándor Pecsora
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On the strong law of large numbers for a stationary sequence [PDF]
, 2016 New conditions of applicability of the strong law of large numbers to a stationary sequence are found by means of recent general results formulated in terms of moments of sums of random variables.
Petrov, Valentin V.
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A strong law of large numbers in credibility theory
, 2006 In this paper, the issue of the law of large numbers for fuzzy variables is considered. Since in credibility theory convergence in credibility implies convergence almost sure, the strong law of large numbers is defined via convergence in credibility ...
Yanju Chen, Yan-kui Liu
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A STRONG LAW OF LARGE NUMBERS FOR MARTINGALES
, 2010 [[abstract]]We derive a moment inequality for the Skorohod representation theorem and apply it to obtain a strong law of large numbers for martingales[[fileno]]2010218010002[[department ...
SHEU, SS;YAO, YS
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