On the strong convergence for weighted sums of ρ~*-mixing random variables

摘要

A complete convergence result is obtained for weighted sums of identically distributed ρ~ *-mixing random variables with E{pipe}X_ 1{pipe}~α log(1 + {pipe}X_ 1{pipe}) <~ ∞ for some 0 < α ≤ 2. This result partially extends the result of Sung (Stat Papers 52: 447-454, 2011) for negatively associated random variables to ρ~*-mixing random variables. It also settles the open problem posed by Zhou et al. (J Inequal Appl, 2011, doi:10.1155/2011/157816).