Abstract
To derive a Baum-Katz-type result, we establish a Chover-type law
of the iterated logarithm for the weighted sums of
Open AccessChover-type laws of the iterated logarithm for weighted
sums of
Chover-type laws of the iterated logarithm for weighted
sums of ρ ∗
Received24 Sept 2004
Revised31 May 2005
Accepted31 May 2005
Published05 Apr 2006
References
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.
View at: Google Scholar | Zentralblatt MATH | MathSciNetP. Y. Chen, “Limiting behavior of weighted sums with stable distributions,” Statistics & Probability Letters, vol. 60, no. 4, pp. 367–375, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetP. Y. Chen and L. H. Huang, “The Chover law of the iterated logarithm for random geometric series of stable distribution,” Acta Mathematica Sinica, vol. 43, no. 6, pp. 1063–1070, 2000 (Chinese).
View at: Google Scholar | Zentralblatt MATHJ. Chover, “A law of the iterated logarithm for stable summands,” Proceedings of the American Mathematical Society, vol. 17, no. 2, pp. 441–443, 1966.
View at: Google Scholar | Zentralblatt MATH | MathSciNetZ. Y. Lin and C. R. Lu, Limit Theory for Mixing Dependent Random Variables, vol. 378 of Mathematics and Its Applications, Kluwer Academic, Dordrecht; Science Press, New York, 1996.
View at: Zentralblatt MATH | MathSciNetZ. Y. Lin, C. R. Lu, and Z. G. Su, Foundation of Probability Limit Theory, Higher Education Press, Beijing, 1999.
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.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. 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.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. 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.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetL. Peng and Y. C. Qi, “Chover-type laws of the iterated logarithm for weighted sums,” Statistics & Probability Letters, vol. 65, no. 4, pp. 401–410, 2003.
View at: Publisher Site | Google Scholar | MathSciNetY. C. Qi and P. Cheng, “A law of the iterated logarithm for partial sums in the field of attraction of a stable law,” Chinese Annals of Mathematics. Series A. Shuxue Niankan. A Ji, vol. 17, no. 2, pp. 195–206, 1996 (Chinese).
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. 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.
View at: Google Scholar | Zentralblatt MATH | MathSciNetK. Vasudeva and G. Divanji, “LIL for delayed sums under a non-identically distributed setup,” Teoriya Veroyatnosteĭ i ee Primeneniya, vol. 37, no. 3, pp. 534–542, 1992 (Russian), translation in Theory Probab. Appl. \textbf{37} (1992), no. 3, 497–506.
View at: Google Scholar | Zentralblatt MATH | MathSciNetN. M. Zinchenko, “A modified law of iterated logarithm for stable random variables,” Theory of Probability and Mathematical Statistics, vol. 49, pp. 69–76 (1995), 1994.
View at: Google Scholar | Zentralblatt MATH | MathSciNet
Copyright
Copyright © 2006 Guang-hui Cai. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.