论文信息 - A Note on the Borel-Cantelli Lemma

A Note on the Borel-Cantelli Lemma

In this short note, we discuss the Barndorﬀ-Nielsen lemma, which is a generalization of well-known Borel-Cantelli lemma. Although the result stated in the Barndorﬀ-Nielsen lemma is correct, it does not follow from the argument proposed in the corre-sponding proof. In this note, we show this and oﬀer an alternative proof of this lemma. We also propose a new generalization of Borel-Cantelli lemma.

N. Balakrishnan | A. Stepanov

[1] A. Stepanov,et al. On the use of the Borel–Cantelli lemma in Markov chains , 2014 .

[2] A. Frolov. On inequalities for probabilities of unions of events and the Borel-Cantelli lemma , 2014 .

[3] A. Frolov,et al. Bounds for probabilities of unions of events and the Borel–Cantelli lemma , 2012 .

[4] A. Stepanov. On the Borel-Cantelli Lemma , 2011, 1110.2577.

[5] T. K. Chandra. The Borel-Cantelli lemma under dependence conditions , 2008 .

[6] A. Stepanov. Generalization of the Borel-Cantelli Lemma , 2006, math/0605007.

[7] V. V. Petrov,et al. A generalization of the Borel–Cantelli Lemma , 2004 .

[8] T. K. Chandra. A First Course in Asymptotic Theory of Statistics , 1999 .

[9] Simon Kochen,et al. A note on the Borel-Cantelli lemma , 1964 .

[10] John Lamperti,et al. Wiener's test and Markov chains , 1963 .

[11] O. Barndorff-Nielsen. ON THE RATE OF GROWTH OF THE PARTIAL MAXIMA OF A SEQUENCE OF INDEPENDENT, IDENTICALLY DISTRIBUTED RANDOM VARIABLES , 1961 .

[12] Angelika Mueller,et al. Principles Of Random Walk , 2016 .

[13] P. Erdos. ON CANTOR ' S SERIES WITH CONVERGENT By , 2004 .

[14] P Erd,et al. On the application of the borel-cantelli lemma , 1952 .