JOURNAL BROWSE
Search
Advanced SearchSearch Tips
PRECISE ASYMPTOTICS IN LOGLOG LAW FOR ρ-MIXING RANDOM VARIABLES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 32, Issue 3,  2010, pp.525-536
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2010.32.3.525
 Title & Authors
PRECISE ASYMPTOTICS IN LOGLOG LAW FOR ρ-MIXING RANDOM VARIABLES
Ryu, Dae-Hee;
  PDF(new window)
 Abstract
Let be identically distributed -mixing random variables with mean zeros and positive finite variances. In this paper, we prove , where and .
 Keywords
Precise asymptotics;Complete moment convergence;mixing;Law of the iterated logarithm;
 Language
English
 Cited by
 References
1.
Baum, L.M. and Katz, M.(1965) Convergence rates in the law of large numbers, Trans. Amer. Soc. 120 108-123 crossref(new window)

2.
Bradley, R.C.(1988) A central limit theorem for p-mixing sequences with infinite variance, Ann. Probab. 18 313-332

3.
Chen, R.C.(1978) A remark on the tail probability of a distribution , J. Multivariate Anal. 8 328-333 crossref(new window)

4.
Davis, J.A.(1968) Convergence rates for the law of the iterated logarithm, Ann. Math. Statist. 39 1479-1485

5.
Erdos(1949) On a theorem of Hsu and Robbins, Ann. Math. Statist. 20 286-291 crossref(new window)

6.
Gut, A. and Spataru, A. (2000) Precise asymptotics in Baum-Katz and Davis law of large numbers, J. Math. Anal. Appl. 248 233-246 crossref(new window)

7.
Heyde, C.C.(1975) A supplement to the strong law of large numbers, J. Appl. Probab. 12 173-175 crossref(new window)

8.
Hsu, P.L. and Robbins, H.(1947) Complete convergence and the law of large numbers, Proc. Nat. Acad. Sci. U.S.A. 33 25-31 crossref(new window)

9.
Huang, W., Jiang, Y. and Zhang, L.X.(2005) Precise asymptotics in the Baum-Katz and Davis Laws of large numbers of $\rho$-mixing sequences. Acta. Math.Sinica(English series) 21 1057-1070 crossref(new window)

10.
Ibragimov, I. A.(1975) A note on the central limit theorem for dependent sequec-nes of random variables, Probab. Theor. Appl. 20 134-139

11.
Kolmogorov, A.N. and Rozanov, U.N.(1960) On the strong mixing conditions of a stationary Gaussian process, Probab. Theory Appl. 2 222-227

12.
Lin, Y. and Lu, C.R.(1996) Limit theorems of mixing dependent random variables, New York, Dordrecht: Science Press, Kluwer, Academic Pub.

13.
Peligrad, M.(1987) The convergence of moments in the central limit theorem for $\rho$-mixing sequence of random variables, Proc. Amer. Math. Soc. 101 142-148

14.
Shao, Q.M.(1995) Maximal inequality for partial sums of $\rho$-mixing sequences, Ann. Probab. 23 948-965 crossref(new window)

15.
Spataru, A.(1999) Precise asymptotics in Spitzer's law of large numbers, J. Theor. Probab. 12 811-819 crossref(new window)

16.
Spitzer, F.(1956) A combinatorial lemma and its applcations to probability theory, Trans. Amer. Soc. 82 323-339 crossref(new window)

17.
Stout, W.F.(1995) Almost sure convergence, Academic, New York

18.
Zhao, Y.(2008) Precise rates in complete moment convergence for $\rho$-mixing sequences, J. Math. Anal. Appl. 339 553-565 crossref(new window)