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Statistica Sinica 10(2000), 1011-1019



STRONG LAWS FOR WEIGHTED SUMS OF RANDOM

ELEMENTS


Han-Ying Liang and Chun Su


Tongji University and University of Science and Technology of China


Abstract: Strong laws of large numbers for weighted sums of independent random variables are proved for Banach spaces of type $p$. Chen, Zhu and Fang's (1996) results on real-valued i.i.d. random variables are extended and generalized, and their unsolved problem is answered. Also, necessary conditions for these strong convergences are considered.



Key words and phrases: Banach space of type $p$, random element, strong law, weighted sum.



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