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.
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.1317 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832547550022860800 |
|---|---|
| author | Le Van Thanh |
| author_facet | Le Van Thanh |
| author_sort | Le Van Thanh |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-0eb6013f01234bd3a626328968d9cee4 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0eb6013f01234bd3a626328968d9cee42025-02-03T06:44:15ZengWileyInternational 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 |
| spellingShingle | Le Van Thanh On the LP-convergence for multidimensional arrays of random variables International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | On the LP-convergence for multidimensional arrays of random variables |
| title_sort | on the lp convergence for multidimensional arrays of random variables |
| url | http://dx.doi.org/10.1155/IJMMS.2005.1317 |
| work_keys_str_mv | AT levanthanh onthelpconvergenceformultidimensionalarraysofrandomvariables |