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 |
| Published: |
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 |
| Summary: | 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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| ISSN: | 0161-1712 1687-0425 |