CONVERGENCE OF DOUBLE SERIES OF RANDOM ELEMENTS IN BANACH SPACES

Title & Authors
CONVERGENCE OF DOUBLE SERIES OF RANDOM ELEMENTS IN BANACH SPACES
Tien, Nguyen Duy; Dung, Le Van;

Abstract
For a double array of random elements $\small{\{X_{mn};m{\geq}1,n{\geq}1\}}$ in a $\small{p}$-uniformly smooth Banach space, $\small{\{b_{mn};m{\geq}1,n{\geq}1\}}$ is an array of positive numbers, convergence of double random series $\small{{\sum}^{\infty}_{m=1}{\sum}^{\infty}_{n=1}X_{mn}}$, $\small{{\sum}^{\infty}_{m=1}{\sum}^{\infty}_{n=1}b^{-1}_{mn}X_{mn}}$ and strong law of large numbers $\small{b^{-1}_{mn}\sum^m_{i=1}\sum^n_{j=1}X_{ij}{\rightarrow}0}$ as $\small{m{\wedge}n{\rightarrow}{\infty}}$ are established.
Keywords
convergence of double random series;strong laws of large numbers;$\small{p}$-uniformly smooth Banach spaces;double array of random elements;
Language
English
Cited by
References
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