文章基本信息

标题：On the LP-convergence for multidimensional arrays of random variables
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作者：Le Van Thanh
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2005
卷号：2005
期号：8
页码：1317-1320
DOI：10.1155/IJMMS.2005.1317
出版社：Hindawi Publishing Corporation
摘要：
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 .