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Hajek-Renyi-type inequality for some nonmonotonic functions of associated random variables. (English) Zbl 1131.60011

Summary: Let \({Y_{n},n\geq 1}\) be a sequence of nonmonotonic functions of associated random variables. We derive a Newman and Wright (1981) type of inequality for the maximum of partial sums of the sequence \({Y_{n},n\geq 1}\) and a Hajek-Renyi-type inequality for nonmonotonic functions of associated random variables under some conditions. As an application, a strong law of large numbers is obtained for nonmonotonic functions of associated random variables.

MSC:

60E15 Inequalities; stochastic orderings
26D15 Inequalities for sums, series and integrals
60F15 Strong limit theorems
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