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On the Borel-Cantelli Lemma and moments. (English) Zbl 1150.60305

Summary: We present some extensions of the Borel-Cantelli Lemma in terms of moments. Our result can be viewed as a new improvement to the Borel-Cantelli Lemma. Our proofs are based on the expansion of moments of some partial sums by using Stirling numbers. We also give a comment concerning the results of V.V.Petrov [Stat.Probab.Lett.67, 233–239 (2004; Zbl 1101.60300)].

MSC:

60A10 Probabilistic measure theory
60F15 Strong limit theorems
05A18 Partitions of sets

Citations:

Zbl 1101.60300
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