×
Zhu, Meng-Hu

Strong laws of large numbers for arrays of rowwise \(\rho ^{\ast }\)-mixing random variables. (English) Zbl 1181.60044

Discrete Dyn. Nat. Soc. 2007, Article ID 74296, 6 p. (2007).
Summary: Some strong laws of large numbers for arrays of rowwise \(\rho ^{\ast }\)-mixing random variables are obtained. The result obtained not only generalizes the result of T.-C. Hu and R. L. Taylor [Int. J. Math. Math. Sci. 20, No. 2, 375–382 (1997; Zbl 0883.60024)] to \(\rho ^{\ast }\)-mixing random variables, but also improves it.

Cited in 2 Reviews
Cited in 9 Documents

MSC:

60F15 Strong limit theorems

Citations:

Zbl 0883.60024
PDF BibTeX XML Cite
\textit{M.-H. Zhu}, Discrete Dyn. Nat. Soc. 2007, Article ID 74296, 6 p. (2007; Zbl 1181.60044)
Full Text: DOI EuDML

References:

[1] T.-C. Hu and R. L. Taylor, “On the strong law for arrays and for the bootstrap mean and variance,” International Journal of Mathematics and Mathematical Sciences, vol. 20, no. 2, pp. 375-382, 1997. · Zbl 0883.60024
[2] W. Bryc and W. Smoleński, “Moment conditions for almost sure convergence of weakly correlated random variables,” Proceedings of the American Mathematical Society, vol. 119, no. 2, pp. 629-635, 1993. · Zbl 0785.60018
[3] M. Peligrad, “On the asymptotic normality of sequences of weak dependent random variables,” Journal of Theoretical Probability, vol. 9, no. 3, pp. 703-715, 1996. · Zbl 0855.60021
[4] M. Peligrad, “Maximum of partial sums and an invariance principle for a class of weak dependent random variables,” Proceedings of the American Mathematical Society, vol. 126, no. 4, pp. 1181-1189, 1998. · Zbl 0899.60044
[5] M. Peligrad and A. Gut, “Almost-sure results for a class of dependent random variables,” Journal of Theoretical Probability, vol. 12, no. 1, pp. 87-104, 1999. · Zbl 0928.60025
[6] S. Utev and M. Peligrad, “Maximal inequalities and an invariance principle for a class of weakly dependent random variables,” Journal of Theoretical Probability, vol. 16, no. 1, pp. 101-115, 2003. · Zbl 1012.60022
[7] P. L. Hsu and H. Robbins, “Complete convergence and the law of large numbers,” Proceedings of the National Academy of Sciences of the United States of America, vol. 33, no. 2, pp. 25-31, 1947. · Zbl 0030.20101
[8] P. Erdös, “On a theorem of Hsu and Robbins,” The Annals of Mathematical Statistics, vol. 20, pp. 286-291, 1949. · Zbl 0033.29001
[9] L. E. Baum and M. Katz, “Convergence rates in the law of large numbers,” Transactions of the American Mathematical Society, vol. 120, no. 1, pp. 108-123, 1965. · Zbl 0142.14802
[10] Y. S. Chow and T. L. Lai, “Some one-sided theorems on the tail distribution of sample sums with applications to the last time and largest excess of boundary crossings,” Transactions of the American Mathematical Society, vol. 208, pp. 51-72, 1975. · Zbl 0335.60021
[11] Y. S. Chow and T. L. Lai, “Paley-type inequalities and convergence rates related to the law of large numbers and extended renewal theory,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 45, no. 1, pp. 1-19, 1978. · Zbl 0397.60030
[12] V. V. Petrov, Limit Theorems of Probability Theory. Sequences of Independent Random Variables, vol. 4 of Oxford Studies in Probability, Oxford University Press, New York, NY, USA, 1995. · Zbl 0826.60001
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.