Complete Convergence for Sums of Arrays of Random Elements
نویسنده
چکیده
Let {Xni} be an array of rowwise independent B-valued random elements and {an} constants such that 0 < an ↑ ∞. Under some moment conditions for the array, it is shown that ∑n i=1Xni/an converges to 0 completely if and only if ∑n i=1Xni/an converges to 0 in probability.
منابع مشابه
Complete Convergence and Some Maximal Inequalities for Weighted Sums of Random Variables
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