Hájek-Rényi-Type Inequality for a Class of Random Variable Sequences and Its Applications (Communications in Mathematical Research, 2021)
In this paper, we obtain the Hájek-Rényi-type inequality for a class ofrandom variable sequences and give some applications for associated random variablesequences, strongly positive dependent stochastic sequences and martingale differencesequences which generalize and improve the results of Prakasa Rao and Soo publishedin Statist. Probab. Lett., 57(2002) and 78(2008). Using this result, we get the integrability of supremum and the strong law of large numbers for a class of randomvariable sequences.
Keywords: Hájek-Rényi-type inequality; associated random variable sequence; strongly positive dependent stochastic sequence; martingale difference sequence.