Results 21 to 30 of about 1,203 (134)
On Chung‐Teicher type strong law for arrays of vector‐valued random variables
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 9, Page 443-458, 2004., 2004 We study the equivalence between the weak and strong laws of large numbers for arrays of row‐wise independent random elements with values in a Banach space ℬ. The conditions under which this equivalence holds are of the Chung or Chung‐Teicher types.
Anna Kuczmaszewska
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Complete convergence for arrays of minimal order statistics
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 44, Page 2325-2329, 2004., 2004 For arrays of independent Pareto random variables, this paper establishes complete convergence for weighted partial sums for the smaller order statistics within each row. This result improves on past strong laws. Moreover, it shows that we can obtain a finite nonzero limit for our normalized partial sums under complete convergence even though the first
André Adler
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Various limit theorems for ratios from the uniform distribution
Open Mathematics, 2016 In this paper, we consider the ratios of order statistics in samples from uniform distribution and establish strong and weak laws for these ratios.
Miao Yu, Sun Yan, Wang Rujun, Dong Manru
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On the order of growth of convergent series of independent random variables
International Journal of Stochastic Analysis, Volume 2004, Issue 2, Page 159-168, 2004., 2004 For independent random variables, the order of growth of the convergent series Sn is studied in this paper. More specifically, if the series Sn converges almost surely to a random variable, the tail series is a well‐defined sequence of random variables and converges to 0 almost surely.
Eunwoo Nam
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Complete convergence for arrays of ratios of order statistics
Open Mathematics, 2019 Let {Xn,k, 1 ≤ k ≤ mn, n ≥ 1} be an array of independent random variables from the Pareto distribution. Let Xn(k) be the kth largest order statistic from the nth row of the array and set Rn,in,jn = Xn(jn)/Xn(in) where jn < in. The aim of this paper is to
Miao Yu +3 more
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A survey of limit laws for bootstrapped sums
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 45, Page 2835-2861, 2003., 2003 Concentrating mainly on independent and identically distributed (i.i.d.) real‐valued parent sequences, we give an overview of first‐order limit theorems available for bootstrapped sample sums for Efron′s bootstrap. As a light unifying theme, we expose by elementary means the relationship between corresponding conditional and unconditional bootstrap ...
Sándor Csörgő, Andrew Rosalsky
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Complete convergence for negatively dependent random variables
International Journal of Stochastic Analysis, Volume 16, Issue 2, Page 121-126, 2003., 2003 In this paper, we study the complete convergence for the means 1n∑i=1nXi and 1nα∑k=1nXnk via. exponential bounds, where α > 0 and {Xn, n ≥ 1} is a sequence of negatively dependent random variables and {Xnk, 1 ≤ k ≤ n, n ≥ 1} is an array of rowwise pairwise negatively dependent random variables.
M. Amini D., A. Bozorgnia
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Sufficient and necessary conditions of convergence for ρ͠ mixing random variables
Open Mathematics, 2019 In the present paper, the sufficient and necessary conditions of the complete convergence and complete moment convergence for ρ͠-mixing random variables are established, which extend some well-known results.
Zhang Shui-Li, Miao Yu, Qu Cong
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Almost sure central limit theorems for strongly mixing and associated random variables
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 3, Page 125-131, 2002., 2002 We prove an almost sure central limit theorem (ASCLT) for strongly mixing sequence of random variables with a slightly slow mixing rate α(n) = O((loglogn)−1−δ). We also show that ASCLT holds for an associated sequence of random variables without a stationarity assumption.
Khurelbaatar Gonchigdanzan
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Complete convergence for weighted sums of pairwise independent random variables
Open Mathematics, 2017 In the present paper, we have established the complete convergence for weighted sums of pairwise independent random variables, from which the rate of convergence of moving average processes is deduced.
Ge Li, Liu Sanyang, Miao Yu
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