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On the second Borel-Cantelli lemma for strongly mixing sequences of events

Part of: Limit theorems

Published online by Cambridge University Press:  14 July 2016

Dirk Tasche
Dirk Tasche*
Affiliation:
Technische Universität Berlin
*
∗Postal address: Ingeborgstrasse 62, 81825 München, Germany.
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Abstract

Assume a given sequence of events to be strongly mixing at a polynomial or exponential rate. We show that the conclusion of the second Borel-Cantelli lemma holds if the series of the probabilities of the events diverges at a certain rate depending on the mixing rate of the events. An application to necessary moment conditions for the strong law of large numbers is given.

Keywords

BOREL-CANTELLI LEMMASTRONG MIXINGSTRONG LAW OF LARGE NUMBERS

MSC classification

Primary: 60F20: Zero-one laws
Secondary: 60F15: Strong theorems
Type
Research Article
Information
Journal of Applied Probability , Volume 34 , Issue 2 , June 1997 , pp. 381 - 394
Copyright
Copyright © Applied Probability Trust 1997 

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