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Keywords:
negatively associated sequence; laws of the iterated logarithm; weighted sum; stable law; Rosental type maximal inequality
negatively associated sequence; laws of the iterated logarithm; weighted sum; stable law; Rosental type maximal inequality
Summary:
To derive a Baum-Katz type result, a Chover-type law of the iterated logarithm is established for weighted sums of negatively associated (NA) and identically distributed random variables with a distribution in the domain of a stable law in this paper.
References:
[1] Chen, P. Y.: Limiting behavior of weighted sums with stable distributions. Statist. Probab. Lett. 60 (2002), 367–375. DOI 10.1016/S0167-7152(02)00286-9 | MR 1947176 | Zbl 1014.60010
[2] Chen, P. Y., Huang, L. H.: The Chover law of the iterated logarithm for random geometric series of stable distribution. Acta Math. Sin. 46 (2000), 1063–1070. (Chinese)
[3] Chover, J. A law of the iterated logarithm for stable summands. Proc. Amer. Math. Soc. 17 (1966), 441–443. DOI 10.1090/S0002-9939-1966-0189096-2 | MR 0189096
[4] Joag, D. K., Proschan, F.: Negative associated random variables with application. Ann. Statist. 11 (1983), 286–295. DOI 10.1214/aos/1176346079 | MR 0684886
[5] Ledoux, M., Talagrand, M.: Probability in Banach Spaces. Springer, Berlin, 1991. MR 1102015
[6] Lin, Z. Y., Lu, C. R.: Limit Theorems on Mixing Random Variables. Kluwer Academic Publishers and Science Press, Dordrecht-Beijing, 1997.
[7] Lin, Z. Y., Lu, C. R., Su, Z. G.: Foundation of Probability Limit Theory. Beijing, Higher Education Press, 1999.
[8] Peng, L., Qi, Y. C.: Chover-type laws of the iterated logarithm for weighted sums. Statist. Probab. Lett. 65 (2003), 401–410. DOI 10.1016/j.spl.2003.08.009 | MR 2039884
[9] Qi, Y. C., Cheng, P.: On the law of the iterated logarithm for the partial sum in the domain of attraction of stable distribution. Chin. Ann. Math., Ser. A 17 (1996), 195–206. (Chinese) MR 1397108
[10] Shao, Q. M.: A comparison theorem on moment inequalities between negatively associated and independent random variables. J. Theor. Probab. 13 (2000), 343–356. DOI 10.1023/A:1007849609234 | MR 1777538 | Zbl 0971.60015
[11] Vasudeva, K., Divanji, G.: LIL for delayed sums under a non-indentically distributed setup. Theory Prob. Appl. 37 (1992), 534–562. MR 1214358
[12] Zhang, L. X., Wen, J. W.: Strong laws for sums of $B$-valued mixing random fields. Chinese Ann. Math. 22A (2001), 205–216. MR 1837525
[13] Zinchenko, N. M.: A modified law of iterated logarithm for stable random variable. Theory Prob. Math. Stat. 49 (1994), 69–76. MR 1445249
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