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Complete convergence for weighted sums of a class of random variables

Deng Xin (Anhui University, School of Mathematical Sciences, Hefei, P.R. China)
Ge Meimei (Anhui University, School of Mathematical Sciences, Hefei, P.R. China)
Wang Xuejun (Anhui University, School of Mathematical Sciences, Hefei, P.R. China)
Liu Yanfang (Anhui University, School of Mathematical Sciences, Hefei, P.R. China)
Zhou Yu (Anhui University, School of Mathematical Sciences, Hefei, P.R. China)

Let {ani,1≤i≤n,n≥1} be an array of real numbers and {Xn,n≥1} be a sequence of random variables satisfying the Rosenthal type inequality, which is stochastically dominated by a random variable X. Under mild conditions, we present some results on complete convergence for weighted sums Σni=1 aniXi of random variables satisfying the Rosenthal type inequality. The results obtained in the paper generalize some known ones in the literatures.

Keywords: complete convergence, weighted sums, Rosenthal type inequality