Journal of Applied Probability

The strong law of large numbers for extended negatively dependent random variables

Yiqing Chen, Anyue Chen, and Kai W. Ng

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Abstract

A sequence of random variables is said to be extended negatively dependent (END) if the tails of its finite-dimensional distributions in the lower-left and upper-right corners are dominated by a multiple of the tails of the corresponding finite-dimensional distributions of a sequence of independent random variables with the same marginal distributions. The goal of this paper is to establish the strong law of large numbers for a sequence of END and identically distributed random variables. In doing so we derive some new inequalities of large deviation type for the sums of END and identically distributed random variables being suitably truncated. We also show applications of our main result to risk theory and renewal theory.

Article information

Source
J. Appl. Probab. Volume 47, Number 4 (2010), 908-922.

Dates
First available in Project Euclid: 4 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1294170508

Digital Object Identifier
doi:10.1239/jap/1294170508

Mathematical Reviews number (MathSciNet)
MR2752902

Zentralblatt MATH identifier
1213.60058

Subjects
Primary: 60F15: Strong theorems
Secondary: 60K05: Renewal theory

Keywords
Asymptotics Borel-Cantelli lemma lower/upper extended negative dependence renewal counting process strong law of large numbers truncation

Citation

Chen, Yiqing; Chen, Anyue; Ng, Kai W. The strong law of large numbers for extended negatively dependent random variables. J. Appl. Probab. 47 (2010), no. 4, 908--922. doi:10.1239/jap/1294170508. https://projecteuclid.org/euclid.jap/1294170508.


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