# On the Borel-Cantelli Lemma and moments

Commentationes Mathematicae Universitatis Carolinae (2006)

- Volume: 47, Issue: 4, page 669-679
- ISSN: 0010-2628

## Access Full Article

top## Abstract

top## How to cite

topAmghibech, S.. "On the Borel-Cantelli Lemma and moments." Commentationes Mathematicae Universitatis Carolinae 47.4 (2006): 669-679. <http://eudml.org/doc/249844>.

@article{Amghibech2006,

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.},

author = {Amghibech, S.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {Borel-Cantelli Lemma; Stirling numbers; Borel-Cantelli Lemma; Stirling numbers},

language = {eng},

number = {4},

pages = {669-679},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {On the Borel-Cantelli Lemma and moments},

url = {http://eudml.org/doc/249844},

volume = {47},

year = {2006},

}

TY - JOUR

AU - Amghibech, S.

TI - On the Borel-Cantelli Lemma and moments

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2006

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 47

IS - 4

SP - 669

EP - 679

AB - 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.

LA - eng

KW - Borel-Cantelli Lemma; Stirling numbers; Borel-Cantelli Lemma; Stirling numbers

UR - http://eudml.org/doc/249844

ER -

## References

top- Chung K.L., Erdös P., On the application of the Borel-Cantelli Lemma, Trans. Amer. Math. Soc. 72 (1952), 1 179-186. (1952) MR0045327
- Erdös P., Rényi A., On Cantor’s series with convergent $\Sigma 1/{q}_{n}$, Ann. Univ. Sci. Budapest Sect. Math. 2 (1959), 93-109. (1959) MR0126414
- Kochen S.P., Stone C.J., A note on the Borel-Cantelli Lemma, Illinois J. Math. 8 (1964), 248-251. (1964) Zbl0139.35401MR0161355
- Lamperti J., Wiener's test and Markov chains, J. Math. Anal. Appl. 6 (1963), 58-66. (1963) Zbl0238.60044MR0143258
- Ortega J., Wschebor M., On the sequence of partial maxima of some random sequences, Stochastic Process. Appl. 16 (1983), 85-98. (1983) MR0723645
- Petrov V.V., A note on the Borel-Cantelli Lemma, Statist. Probab. Lett. 58 (2002), 3 283-286. (2002) Zbl1017.60004MR1921874
- Petrov V.V., A generalization of the Borel-Cantelli Lemma, Statist. Probab. Lett. 67 (2004), 3 233-239. (2004) Zbl1101.60300MR2053525
- Rényi A., Probability Theory, North-Holland Series in Applied Mathematics and Mechanics, vol. 10, North-Holland, Amsterdam-London, 1970; German version 1962, French version 1966, new Hungarian edition 1965. MR0315747
- Spitzer F., Principles of Random Walk, 2nd edition, Springer, New York-Heidelberg, 1976. Zbl0979.60002MR0388547
- Van Lint J.H., Wilson R.M., A Course in Combinatorics, 2nd ed., Cambridge University Press, Cambridge, 2001. Zbl0980.05001MR1871828

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.