Marcinkiewicz-type strong law of large numbers for double arrays of pairwise independent random variables
1999 ◽
Vol 22
(1)
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pp. 171-177
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Keyword(s):
Let {Xij}be a double sequence of pairwise independent random variables. If P{|Xmn|≥t}≤P{|X|≥t}for all nonnegative real numbers tandE|X|p(log+|X|)3<∞, for1<p<2, then we prove that∑i=1m∑j=1n(Xij−EXij)(mn)1/p→0 a.s. as m∨n→∞. (0.1)Under the weak condition ofE|X|plog+|X|<∞, it converges to 0inL1. And the results can be generalized to anr-dimensional array of random variables under the conditionsE|X|p(log+|X|)r+1<∞,E|X|p(log+|X|)r−1<∞, respectively, thus, extending Choi and Sung's result [1] of the one-dimensional case.
1995 ◽
Vol 75
(5)
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pp. 1944-1946
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1995 ◽
Vol 25
(1)
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pp. 21-26
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2013 ◽
Vol 142
(2)
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pp. 502-518
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2012 ◽
Vol 05
(01)
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pp. 1250007
1997 ◽
Vol 86
(5-6)
◽
pp. 1373-1384
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Keyword(s):
2010 ◽
Vol 47
(04)
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pp. 908-922
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