On the LP-convergence for multidimensional arrays of random variables
For a d-dimensional array of random variables {Xn,n∈ℤ+d} such that {|Xn|p,n∈ℤ+d} is uniformly integrable for some 0<p<2, the Lp-convergence is established for the sums (1/|n|1/p) (∑j≺n(Xj−aj)), where aj=0 if 0<p<1, and aj=EXj if 1≤p<2.
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.1317 |
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doaj-0eb6013f01234bd3a626328968d9cee42020-11-24T23:50:07ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-01200581317132010.1155/IJMMS.2005.1317On the LP-convergence for multidimensional arrays of random variablesLe Van Thanh0Department of Mathematics, Vinh University, Nghe An 42118, VietnamFor a d-dimensional array of random variables {Xn,n∈ℤ+d} such that {|Xn|p,n∈ℤ+d} is uniformly integrable for some 0<p<2, the Lp-convergence is established for the sums (1/|n|1/p) (∑j≺n(Xj−aj)), where aj=0 if 0<p<1, and aj=EXj if 1≤p<2.http://dx.doi.org/10.1155/IJMMS.2005.1317 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Le Van Thanh |
| spellingShingle |
Le Van Thanh On the LP-convergence for multidimensional arrays of random variables International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Le Van Thanh |
| author_sort |
Le Van Thanh |
| title |
On the LP-convergence for multidimensional arrays of random variables |
| title_short |
On the LP-convergence for multidimensional arrays of random variables |
| title_full |
On the LP-convergence for multidimensional arrays of random variables |
| title_fullStr |
On the LP-convergence for multidimensional arrays of random variables |
| title_full_unstemmed |
On the LP-convergence for multidimensional arrays of random variables |
| title_sort |
on the lp-convergence for multidimensional arrays of random variables |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2005-01-01 |
| description |
For a d-dimensional array of random variables
{Xn,n∈ℤ+d} such that {|Xn|p,n∈ℤ+d} is uniformly integrable
for some 0<p<2, the Lp-convergence is established for the sums (1/|n|1/p) (∑j≺n(Xj−aj)), where aj=0 if 0<p<1, and aj=EXj if 1≤p<2. |
| url |
http://dx.doi.org/10.1155/IJMMS.2005.1317 |
| work_keys_str_mv |
AT levanthanh onthelpconvergenceformultidimensionalarraysofrandomvariables |
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1725479930197704704 |