A supplement to the Baum-Katz-Spitzer complete convergence theorem

作者：Li, De Li^*; Zhang, Fu Xing; Rosalsky, Andrew

来源：Acta Mathematica Sinica-English Series, 2007, 23(3): 557-562.

DOI：10.1007/s10114-005-0823-y

• partial sums of i.i.d. Banach space valued random variables
• Baum-Katz-Spitzer complete convergence theorem
• almost sure convergence

Let {X, X-n; n >= 1} be a sequence of i.i.d. Banach space valued random variables and let {an; n >= 1} be a sequence of positive constants such that
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Set S-n = Sigma(n)(i=1) X-i, n >= 1. In this paper we prove that
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if and only if
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This result generalizes the Baum-Katz-Spitzer complete convergence theorem. Combining our result and a corollary of Einmahl and Li, we solve a conjecture posed by Gut.

• 出版日期2007-3
• 单位邵阳学院