| Title:
|
Chover-type laws of the iterated logarithm for weighted sums of NA sequences (English) |
| Author:
|
Cai, Guang-hui |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
132 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
27-33 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
negatively associated sequence |
| Keyword:
|
laws of the iterated logarithm |
| Keyword:
|
weighted sum |
| Keyword:
|
stable law |
| Keyword:
|
Rosental type maximal inequality |
| MSC:
|
60F15 |
| MSC:
|
62G50 |
| idZBL:
|
Zbl 1174.60328 |
| idMR:
|
MR2311750 |
| DOI:
|
10.21136/MB.2007.133994 |
| . |
| Date available:
|
2009-09-24T22:28:40Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133994 |
| . |
| Reference:
|
[1] Chen, P. Y.: Limiting behavior of weighted sums with stable distributions.Statist. Probab. Lett. 60 (2002), 367–375. Zbl 1014.60010, MR 1947176, 10.1016/S0167-7152(02)00286-9 |
| Reference:
|
[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) |
| Reference:
|
[3] : Chover, J. A law of the iterated logarithm for stable summands.Proc. Amer. Math. Soc. 17 (1966), 441–443. MR 0189096, 10.1090/S0002-9939-1966-0189096-2 |
| Reference:
|
[4] Joag, D. K., Proschan, F.: Negative associated random variables with application.Ann. Statist. 11 (1983), 286–295. MR 0684886, 10.1214/aos/1176346079 |
| Reference:
|
[5] Ledoux, M., Talagrand, M.: Probability in Banach Spaces.Springer, Berlin, 1991. MR 1102015 |
| Reference:
|
[6] Lin, Z. Y., Lu, C. R.: Limit Theorems on Mixing Random Variables.Kluwer Academic Publishers and Science Press, Dordrecht-Beijing, 1997. |
| Reference:
|
[7] Lin, Z. Y., Lu, C. R., Su, Z. G.: Foundation of Probability Limit Theory.Beijing, Higher Education Press, 1999. |
| Reference:
|
[8] Peng, L., Qi, Y. C.: Chover-type laws of the iterated logarithm for weighted sums.Statist. Probab. Lett. 65 (2003), 401–410. MR 2039884, 10.1016/j.spl.2003.08.009 |
| Reference:
|
[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 |
| Reference:
|
[10] Shao, Q. M.: A comparison theorem on moment inequalities between negatively associated and independent random variables.J. Theor. Probab. 13 (2000), 343–356. Zbl 0971.60015, MR 1777538, 10.1023/A:1007849609234 |
| Reference:
|
[11] Vasudeva, K., Divanji, G.: LIL for delayed sums under a non-indentically distributed setup.Theory Prob. Appl. 37 (1992), 534–562. MR 1214358 |
| Reference:
|
[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 |
| Reference:
|
[13] Zinchenko, N. M.: A modified law of iterated logarithm for stable random variable.Theory Prob. Math. Stat. 49 (1994), 69–76. MR 1445249 |
| . |
