On the LP-convergence for multidimensional arrays of random variables
Le Van Thanh1
Received14 Aug 2004
Revised04 Mar 2005
Abstract
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.