Complete Convergence of Weighted Sums for $\rho^*$-Mixing Sequence of Random Variables
Received:May 06, 2012  Revised:September 03, 2012
Key Word: $\rho^*$-mixing sequence of random variables   weighted sums   complete convergence   moment inequality.
Fund ProjectL:Supported by the National Natural Science Foundation of China\,(Grant Nos.11271020; 11201004), the Key Project of Chinese Ministry of Education (Grant No.211077) and the Natural Science Foundation of Anhui Province (Grant Nos.10040606Q30; 1208085MA11).
 Author Name Affiliation Mingle GUO School of Mathematics and Computer Science, Anhui Normal University, Anhui 241003, P. R. China Dongjin ZHU School of Mathematics and Computer Science, Anhui Normal University, Anhui 241003, P. R. China
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In this paper, the complete convergence of weighted sums for $\rho^*$-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete convergence of weighted sums for $\rho^*$-mixing sequence of random variables are established. We not only promote and improve the results of Li et al. (J. Theoret. Probab., 1995, {\bf 8}(1): 49--76) from i.i.d. to $\rho^*$-mixing setting but also obtain their necessities and relax their conditions.