On the strong convergence for weighted sums of ρ <Superscript>*</Superscript>-mixing random variables

A complete convergence result is obtained for weighted sums of identically distributed ρ <Superscript>*</Superscript>-mixing random variables with E|X <Subscript>1</Subscript>|<Superscript> α </Superscript> log(1 + |X <Subscript>1</Subscript>|) > ∞ for some 0 > α ≤ 2. This result partially extends the result of Sung (Stat Papers 52: 447–454, <CitationRef CitationID="CR14">2011</CitationRef>) for negatively associated random variables to ρ <Superscript>*</Superscript>-mixing random variables. It also settles the open problem posed by Zhou et al. (J Inequal Appl, <CitationRef CitationID="CR18">2011</CitationRef>, doi:<ExternalRef> <RefSource>10.1155/2011/157816</RefSource> <RefTarget Address="10.1155/2011/157816" TargetType="DOI"/> </ExternalRef>). Copyright Springer-Verlag 2013