Complete convergence of weighted sums for arrays of rowwise \(\varphi \)-mixing random variables.
The authors consider arrays of rowwise \(\varphi\)-mixing random variables and study necessary and sufficient conditions under which weighted sums of such random variables converge completely and satisfy also the complete moment convergence. Using the standard technique, they establish a variant of the Baum-Katz-type theorem for these arrays of weakly dependent random variables and generalize some recent results in this field (see [\textit{X.-J. Wang} and \textit{S.-H. Hu}, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 106, No. 1, 321--331 (2012; Zbl 1266.60056)]).
Marcinkiewicz-Zygmund strong law of large numbers
scientific article; zbMATH DE number 6391452
scientific article