Hájek-Rényi-Type Inequality for a Class of Random Variable Sequences and Its Applications

Abstract

In this paper, we obtain the Hájek-Rényi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in 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 random variable sequences.