On the L P -convergence for multidimensional arrays of random variables

Le Van Thanh

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-4

Abstract:

For a d -dimensional array of random variables { X n , n ∈ ℤ + d } such that { | X n | p , n ∈ ℤ + d } is uniformly integrable for some 0 < p < 2 , the L p -convergence is established for the sums ( 1 / | n | 1 / p ) ( ∑ j ≺ n ( X j − a j ) ) , where a j = 0 if 0 < p < 1 , and a j = E X j if 1 ≤ p < 2 .

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:267043

DOI: 10.1155/IJMMS.2005.1317

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