Journal of University of Chinese Academy of Sciences >
The law of the iterated logarithm for random sums of a double random sequence
Received date: 2010-06-15
Revised date: 2010-09-16
Online published: 2011-07-15
We have obtained the law of the iterated logarithm for random sums of a double sequence of random variables {ξn,j; n≥1,j≥1}, where {ξn,j; n≥1,j≥1} are independent and for any fixed n, {ξn,j; j≥1} have the same distribution.
GAO Zhen-Long , HU Xiao-Yu . The law of the iterated logarithm for random sums of a double random sequence[J]. Journal of University of Chinese Academy of Sciences, 2011 , 28(4) : 424 -430 . DOI: 10.7523/j.issn.2095-6134.2011.4.002
[1] Stout W F. Almost sure convergence
[M]. New York:Academic Press, 1974.
[2] Gut A. Law of the iterated logarithm for subsequences
[J]. Probab Math Statist, 1986, 7(1): 27-58.
[3] Schwabe R,Gut A. On the law of the iterated logarithm for rapidly increasing subsequences
[J]. Math Nachr, 1996, 178(2): 309-320.
[4] Torrang I. Law of the iterated logarithm- cluster points of deterministic and random subsequences
[J]. Probab Math Statist, 1987, 8(1): 133-141.
[5] Chow Y S, Teicher S, Wei C Z, et al. Iterated logarithm laws with random subsequences
[J]. Z W Verw Gebiete, 1981, 57(2): 235-251.
[6] Divanji G. Law of iterated logarithm and almost sure limit points for random sums
[J]. Stitist Meth, 2006, 3: 398-405.
[7] Vasudeva R, Divanji G. Law of iterated logarithm for random subsequences
[J]. Stitist Probab Lett,1991, 12: 189-194.
[8] Gut A. Convergence rates for probabilities of moderate deviations for sums of random variables with multidimensional indices
[J]. Ann Prob, 1980, 8(1/2): 298-313.
[9] 胡晓予. 高等概率论
[M]. 北京: 科学出版社,2009.
/
| 〈 |
|
〉 |