×

On the strong rates of convergence for arrays of rowwise negatively dependent random variables. (English) Zbl 1223.60023

The now classical Hsu-Robbins-Erdős-Spitzer-Baum-Katz theorem concerns moment conditions for the convergence of \[ \sum^\infty_{n=1} n^{(r/p)- 2} P(|S_n|>\varepsilon n^{1/p}), \] where \(r> 0\), \(0< p< 2\), \(r\geq p\) and where \(S_n\) is a sum of \(n\) i.i.d. random variables. This result has been extended in various directions over the last couple of decades.
In the present paper \(S_n\) is replaced by \(S_{k_n}\) which, for every \(n\), is a sum of the \(k\), negatively dependent random variables of the \(n\)th row of an array, and the weights are more general than powers.

MSC:

60F15 Strong limit theorems
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] DOI: 10.1137/S0040585X97983079 · Zbl 1146.60025
[2] DOI: 10.1016/j.spl.2004.11.006 · Zbl 1087.60030
[3] DOI: 10.1073/pnas.33.2.25 · Zbl 0030.20101
[4] DOI: 10.1214/aoms/1177730037 · Zbl 0033.29001
[5] DOI: 10.1214/aoms/1177729897 · Zbl 0035.21403
[6] Gut , A. 1994 . Complete convergence. In: Asymptotic Statistics (Prague, 1993),Contrib. Statist., Physica, Heidelberg , pp. 237 – 247 .
[7] DOI: 10.1016/S0167-7152(98)00150-3 · Zbl 0910.60017
[8] DOI: 10.1016/j.spl.2006.04.006 · Zbl 1100.60014
[9] DOI: 10.1016/S0167-7152(99)00209-6
[10] DOI: 10.4134/CKMS.2003.18.2.375 · Zbl 1101.60324
[11] DOI: 10.1016/j.spl.2003.11.010 · Zbl 1074.60038
[12] Studia Math. 52 pp 159– (1974)
[13] DOI: 10.1023/A:1007849609234 · Zbl 0971.60015
[14] DOI: 10.1214/aos/1176346079 · Zbl 0508.62041
[15] Bozorgnia A., Proceedings of the First World Congress of Nonlinear Analysts pp 1639– (1996)
[16] DOI: 10.1081/SAP-120004118 · Zbl 1003.60032
[17] Volodin A., Pakistan Journal of Statistics 18 pp 249– (2002)
[18] Ahmed E., Lobachevskii Journal of Mathematics 18 pp 3– (2005)
[19] Gan S. X., Acta. Math. Sci. 28 pp 283– (2008)
[20] Gan , S. , Chen , P. , and Qiu , D. Rosenthal inequality for negatively dependent sequences and its applications. Unpublished manuscript. · Zbl 1249.60022
[21] DOI: 10.1214/aoms/1177699260 · Zbl 0146.40601
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.