Complete convergence for weighted sums of arrays of random elements
Let {Xnk:k,n=1,2,…} be an array of row-wise independent random elements in a separable Banach space. Let {ank:k,n=1,2,…} be an array of real numbers such that ∑k=1∞|ank|≤1 and ∑n=1∞exp(−α/An)<∞ for each α ϵ R+ where An=∑k=1∞ank2. The complete convergence of ∑k=1∞ankXnk is obtained under varying m...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1983-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171283000046 |