Marcinkiewicz-type strong law of large numbers for double arrays of pairwise independent random variables
Let {Xij} be a double sequence of pairwise independent random variables. If P{|Xmn|≥t}≤P{|X|≥t} for all nonnegative real numbers t and E|X|p(log+|X|)3<∞, for 1<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...
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Wiley
1999-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171299221710 |
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| author | Dug Hun Hong Seok Yoon Hwang |
| author_facet | Dug Hun Hong Seok Yoon Hwang |
| author_sort | Dug Hun Hong |
| collection | DOAJ |
| description | Let {Xij} be a double sequence of pairwise independent random variables. If P{|Xmn|≥t}≤P{|X|≥t} for all nonnegative real numbers t and E|X|p(log+|X|)3<∞, for 1<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 of E|X|plog+|X|<∞, it converges to 0 in L1. And the results can be generalized to an r-dimensional array of random variables under the conditions E|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. |
| format | Article |
| id | doaj-art-192f1af5cc1b46c79725da2a8333c4ee |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-192f1af5cc1b46c79725da2a8333c4ee2025-02-03T06:07:29ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251999-01-0122117117710.1155/S0161171299221710Marcinkiewicz-type strong law of large numbers for double arrays of pairwise independent random variablesDug Hun Hong0Seok Yoon Hwang1School of Mechanical and Automotive Engineering, Catholic University of Taegu-Hyosung, Kyungbuk 712-702, South KoreaDepartment of Mathematics, Taegu University, Kyungbuk 713-714, South KoreaLet {Xij} be a double sequence of pairwise independent random variables. If P{|Xmn|≥t}≤P{|X|≥t} for all nonnegative real numbers t and E|X|p(log+|X|)3<∞, for 1<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 of E|X|plog+|X|<∞, it converges to 0 in L1. And the results can be generalized to an r-dimensional array of random variables under the conditions E|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.http://dx.doi.org/10.1155/S0161171299221710Strong law of large numberspairwise independent. |
| spellingShingle | Dug Hun Hong Seok Yoon Hwang Marcinkiewicz-type strong law of large numbers for double arrays of pairwise independent random variables International Journal of Mathematics and Mathematical Sciences Strong law of large numbers pairwise independent. |
| title | Marcinkiewicz-type strong law of large numbers for double arrays of pairwise independent random variables |
| title_full | Marcinkiewicz-type strong law of large numbers for double arrays of pairwise independent random variables |
| title_fullStr | Marcinkiewicz-type strong law of large numbers for double arrays of pairwise independent random variables |
| title_full_unstemmed | Marcinkiewicz-type strong law of large numbers for double arrays of pairwise independent random variables |
| title_short | Marcinkiewicz-type strong law of large numbers for double arrays of pairwise independent random variables |
| title_sort | marcinkiewicz type strong law of large numbers for double arrays of pairwise independent random variables |
| topic | Strong law of large numbers pairwise independent. |
| url | http://dx.doi.org/10.1155/S0161171299221710 |
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