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The Strong Law of Large Numbers for Extended Negatively Dependent Random Variables

Part of: Special processes Limit theorems

Published online by Cambridge University Press:  14 July 2016

Yiqing Chen ,
Anyue Chen  and
Kai W. Ng
Yiqing Chen*
Affiliation:
University of Liverpool
Anyue Chen*
Affiliation:
Xi'an Jiaotong-Liverpool University
Kai W. Ng*
Affiliation:
The University of Hong Kong
*
∗ Postal address: Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, UK.
∗ Postal address: Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, UK.
∗∗∗ Postal address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong.
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Abstract

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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.

Keywords

AsymptoticsBorel-Cantelli lemmalower/upper extended negative dependencerenewal counting processstrong law of large numberstruncation

MSC classification

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

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 4 , December 2010 , pp. 908 - 922
Copyright
Copyright © Applied Probability Trust 2010 

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