Double arrays of random elements Martingale type p Banach spaces Weak laws of large numbers Weighted double sums
Issue Date:
2010
Publisher:
Bulletin of the Korean Mathematical Society
Citation:
Volume: 47, Issue: 3, Page : 467-482
Abstract:
For a double array of random elements {Vmn;m ? 1, n ? 1} in a real separable Banach space, some
mean convergence theorems and weak laws of large numbers are established. For the mean convergence
results, conditions are provided under which The weak law results provide conditions for in probability
where {Tm;m ? 1} and {Tn; n ? 1} are sequences of positive integer-valued random variables, {kmn;m ? 1,
n ? 1} is an array of positive integers. The sharpness of the results is illustrated by examples. ?? 2010 The
Korean Mathematical Society.
