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Best Possible Sufficient Conditions for Strong Law of Large Numbers for Multi-Indexed Orthogonal Random Elements

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  • Kuo-Liang Su

Abstract

It will be shown and induced that the d -dimensional indices in the Banach spaces version conditions ∑ n ( E ‖ X n ‖ p / | n α | p ) < ∞ are sufficient to yield lim min 1 ≤ j ≤ d ( n j ) → ∞ ( 1 / | n α | ) ∑ k ≤ n ∏ j = 1 d ( 1 − ( k j − 1 ) / n j ) X k = 0 a.s. for arrays of James-type orthogonal random elements. Particularly, it will be shown also that there are the best possible sufficient conditions for multi-indexed independent real-valued random variables.

Suggested Citation

  • Kuo-Liang Su, 2007. "Best Possible Sufficient Conditions for Strong Law of Large Numbers for Multi-Indexed Orthogonal Random Elements," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2007, pages 1-15, April.
    • Handle: RePEc:hin:jijmms:086909
    DOI: 10.1155/2007/86909
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