On estimation for probabilities of unions of events with applications to the Borel-Cantelli lemma

Authors

  • Andrey N. Frolov St. Petersburg State University, Universitetskaya nab., 7-9, St. Petersburg, 199034, Russian Federation;

Abstract

We discuss a method which allow to estimate probabilities of unions of events from above and below. We derive new upper and lower bounds for such probabilities. These bounds are sharp. They are generalizations of the previous ones. They are based on moments of the sums of indicators of the events. The order of these moments may be non-integer. Non-power moments may be applied as well. We discuss applications of our inequalities to generalizations of the first and second parts of the Borel-Cantelli lemma. The method may be applied in arbitrary measurable spaces as well. Refs 18.

Keywords:

Bonferroni inequalities, probabilities of unions of events, Borel-Cantelli lemma

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Published

2015-08-01

How to Cite

Frolov, A. N. (2015). On estimation for probabilities of unions of events with applications to the Borel-Cantelli lemma. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2(3), 387–393. Retrieved from https://math-mech-astr-journal.spbu.ru/article/view/11173

Issue

Vol. 2 No. 3 (2015)

Section

Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.