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Inequalities of maximum of partial sums and weak convergence for a class of weak dependent random variables. (English) Zbl 1102.60023
Summary: We establish a Rosenthal-type inequality of the maximum of partial sums for \(\rho^-\)-mixing random fields. As its applications we get the Hájek-Rényi inequality and weak convergence of sums of \(\rho^-\)-mixing sequence. These results extend related results for NA sequences and \(\rho^*\)-mixing random fields.

MSC:
60F05 Central limit and other weak theorems
60E15 Inequalities; stochastic orderings
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