Open Access Research

Limit theorems for delayed sums of random sequence

Ding Fang-qing1 and Wang Zhong-zhi2*

Author Affiliations

1 Department of Mathematics & Physics, HeFei University, HeFei 230601, P. R. China

2 Faculty of Mathematics & Physics, AnHui University of Technology, Ma'anshan 243002, P. R. China

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Journal of Inequalities and Applications 2012, 2012:124 doi:10.1186/1029-242X-2012-124

Published: 31 May 2012

Abstract

For a sequence of arbitrarily dependent random variables (Xn)n∈N and Borel sets (Bn)n∈N, on real line the strong limit theorems, represented by inequalities, i.e. the strong deviation theorems of the delayed average <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/124/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/124/mathml/M1">View MathML</a> are investigated by using the notion of asymptotic delayed log-likelihood ratio. The results obtained popularizes the methods proposed by Liu.

Mathematics Subject Classification 2000: Primary, 60F15.

Keywords:
strong deviation theorem; likelihood ratio; delayed sums