ON THE COMPLETE MOMENT CONVERGENCE OF MOVING AVERAGE PROCESSES GENERATED BY ρ*-MIXING SEQUENCES

Title & Authors
ON THE COMPLETE MOMENT CONVERGENCE OF MOVING AVERAGE PROCESSES GENERATED BY ρ*-MIXING SEQUENCES
Ko, Mi-Hwa; Kim, Tae-Sung; Ryu, Dae-Hee;

Abstract
Let {$\small{Y_{ij}-{\infty}\;}$<$\small{\;i\;}$<$\small{\;{\infty}}$} be a doubly infinite sequence of identically distributed and $\small{{\rho}^*}$-mixing random variables with zero means and finite variances and {$\small{a_{ij}-{\infty}\;}$<$\small{\;i\;}$<$\small{\;{\infty}}$} an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of {${\sum}^n_{k Keywords moving average process;complete moment convergence;$\small{{\rho}^*}$-mixing;moment inequality; Language English Cited by 1. Complete moment convergence for moving average process generated by ρ −$\rho^{-}$-mixing random variables, Journal of Inequalities and Applications, 2015, 2015, 1 2. Convergence of Moving Average Processes for Dependent Random Variables, Communications in Statistics - Theory and Methods, 2011, 40, 13, 2366 3. Complete moment convergence of widely orthant dependent random variables, Communications in Statistics - Theory and Methods, 2017, 46, 14, 7256 References 1. J. I. Baek, T. S. Kim, and H. Y. Liang, On the convergence of moving average processes under dependent conditions, Aust. N. Z. J. Statist. 45 (2003), 331-342 2. R. C. Bradley, Equivalent mixing conditions for random fields, Ann. Probab. 21 (1993), 1921-1926 3. C. W. Bryc and W. Smolenski, Moment conditions for almost sure convergence of weakly correlated random variables, Proc. Amer. Math. Soc. 119 (1993), 629-635 4. R. M. Burton and H. Dehling, Large deviation for some weakly dependent random process, Statist. Probab. Lett. 9 (1990), 397-401 5. Y. S. Chow, On the rate of moment convergence of sample sums and extremes, Bull. Inst. Math. Acad. Sinica 16 (1988), 177-201 6. I. A. Ibragimov, Some limit theorems for stationary processes, Theory Probab. Appl. 7 (1962), 349-382 7. D. L. Li, M. B. Rao, and X. C.Wang, Complete convergence of moving average processes, Statist. Probab. Lett. 14 (1992), 111-114 8. Y. X. Li and L. X. Zhang, Complete moment convergence of moving average processes under dependence assumptions, Statist. Probab. Lett. 70 (2004), 191-197 9. H. Y. Liang, Complete convergence for weighted sums of negatively associated random variables, Statist. Probab. Lett. 48 (2000), 317-325 10. C. Miller, Three theorems on$\rho\$*-mixing random fields, J. Theor. Probab. 7 (1994), 867-882

11.
M. Peligrad and A. Gut, Almost sure results for a class of dependent random variables, J. Theor. Prob. 12 (1999), 87-104

12.
L. X. Zhang, Complete convergence of moving average processes under dependence assumptions, Statist. Probab. Lett. 30 (1996), 165-170