Abstract: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 Petrov V.V., {A generalization of the Borel-Cantelli Lemma}, Statist. Probab. Lett. {67} (2004), no. 3, 233--239.
Keywords: Borel-Cantelli Lemma, Stirling numbers
AMS Subject Classification: Primary 60A10, 60F15; Secondary 05A18