Geodesic
Limiting behaviour of moving average processes based on a sequence of $\rho^-$ mixing and negatively associated random variables
Lobachevskii journal of mathematics, Tome 26 (2007), pp. 17-25 
K. Budsaba; P. Chen; A. I. Volodin. Limiting behaviour of moving average processes based on a sequence of $\rho^-$ mixing and negatively associated random variables. Lobachevskii journal of mathematics, Tome 26 (2007), pp. 17-25. http://geodesic.mathdoc.fr/item/LJM_2007_26_a2/
@article{LJM_2007_26_a2,
     author = {K. Budsaba and P. Chen and A. I. Volodin},
     title = {Limiting behaviour of moving average processes based on a~sequence of $\rho^-$ mixing and negatively associated random variables},
     journal = {Lobachevskii journal of mathematics},
     pages = {17--25},
     year = {2007},
     volume = {26},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2007_26_a2/}
}
TY  - JOUR
AU  - K. Budsaba
AU  - P. Chen
AU  - A. I. Volodin
TI  - Limiting behaviour of moving average processes based on a sequence of $\rho^-$ mixing and negatively associated random variables
JO  - Lobachevskii journal of mathematics
PY  - 2007
SP  - 17
EP  - 25
VL  - 26
UR  - http://geodesic.mathdoc.fr/item/LJM_2007_26_a2/
LA  - en
ID  - LJM_2007_26_a2
ER  - 
%0 Journal Article
%A K. Budsaba
%A P. Chen
%A A. I. Volodin
%T Limiting behaviour of moving average processes based on a sequence of $\rho^-$ mixing and negatively associated random variables
%J Lobachevskii journal of mathematics
%D 2007
%P 17-25
%V 26
%U http://geodesic.mathdoc.fr/item/LJM_2007_26_a2/
%G en
%F LJM_2007_26_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\{Y_i,-\infty$ be a doubly infinite sequence of identically distributed $\rho^-$-mixing or negatively associated random variables, $\{a_i,-\infty$ a sequence of real numbers. In this paper, we prove the rate of convergence and strong law of large numbers for the partial sums of moving average processes $\{\sum_{i=-\infty}^\infty a_iY_{i+n},n\ge1\}$ under some moment conditions.

[1] Bryc W. and Smolenski W., “Moment conditions for almost sure convergence of weakly correlated random variables”, Proc. Amer. Math. Soc., 119 (1993), 629–635 | DOI | MR | Zbl

[2] Budsaba K., Chen P., and Volodin A., “Limiting behaviour of moving average processes based on a sequence of $\rho^-$ mixing random variables”, Thai Statistician: Journal of Thailand Statistical Association, 2007 (to appear) | Zbl

[3] Burton R. M. and Dehling H., “Large deviations for some weakly dependent random processes”, Statist. Probab. Lett., 9 (1990), 397–401 | DOI | MR | Zbl

[4] Ibragimov I. A., “Some limit theorem for stationary processes”, Theory Probab. Appl., 7 (1962), 349–382 | DOI | MR | Zbl

[5] Joag-Dev K. and Proschan F., “Negative association of random variables with applications”, Ann. Statist., 11 (1983), 286–295 | DOI | MR

[6] Li D., Rao M. B., and Wang X. C., “Complete convergence of moving average processes”, Statist. Probab. Lett., 14 (1992), 111–114 | DOI | MR | Zbl

[7] Loève M., Probability Theory II, 4 edition, Spring-Verlag, New York, 1978 | MR | Zbl

[8] Móricz F. A., Serfling R. J., Stout W. F., “Moment and probability bounds with quasisuperadditive structure for the maximum partial sum”, Ann. Probab., 10 (1982), 1032–1040 | DOI | MR | Zbl

[9] Seneta. E., Regularly varying functions, Lecture Notes in Math., 508, Springer, Berlin, 1976 | MR | Zbl

[10] Shao Q. M., “A comparison theorem on inequalities between negatively associated and independent random variables”, J. Theor. Probab., 13 (2000), 343–356 | DOI | MR | Zbl

[11] Wang J. F. and Lu F. B., “Inequalities of maximum of partial sums and weak convergence for a class of weak dependent random variables”, Acta Math. Sin. (Engl. Ser.), 22 (2006), 693–700 | DOI | MR | Zbl