Abstract
We present a generalization of Baum-Katz theorem for negatively associated random variables satisfying some cover condition.
Similar content being viewed by others
References
I. E. Baum and M. Katz, Convergence rates in the law of large numbers, Trans. Amer. Math. Soc., 120 (1965), 108–123.
Y. S. Chow, Delayed sums and Borel summability of independent, identically distributed random variables, Bull. Inst. Math. Acad. Sinica, (1973), 207–2020.
P. Erdős, On a theorem of Hsu and Robbins, Ann. Math. Statistics, 20 (1949), 286–291.
A. Gut, Complete convergence for arrays, Periodica Math. Hungar., 25 (1992), 51–75.
P. L. Hsu and H. Robbins, Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. USA, 33 (1947), 25–31.
T. C. Hu, F. Móricz and R. L. Taylor, Strong laws of large numbers for arrays of rowwise independent random variables, Acta Math. Hungar., 54 (1989), 153–162.
K. Joag-Dev and F. Proschan, Negative association of random variables with applications, Ann. Statist., 11 (1983), 286–295.
M. L. Katz, The probability in the tail of a distribution, Ann. Math. Statist., 34 (1963), 312–318.
M. Peligrad and A. Gut, Almost-sure results for a class of dependent random variables, J. Theor. Probab., 12 (1999), 87–104.
A. R. Pruss, Randomly sampled Riemann sums and complete convergence in the law of large numbers for a case without identical distribution, Proc. Amer. Math. Soc., 124 (1996), 919–929.
Q. M. Shao, A comparison theorem on moment inequalities between negatively associated and independent random variables, J. Theor. Probab., 13 (2000), 343–356.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kuczmaszewska, A. On complete convergence in Marcinkiewicz-Zygmund type SLLN for negatively associated random variables. Acta Math Hung 128, 116–130 (2010). https://doi.org/10.1007/s10474-009-9166-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-009-9166-y