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Maximal inequalities and laws of large numbers for Lq-mixingale arrays

By Yanjiao Meng and Zhengyan Lin

Abstract

In this paper we obtain two inequalities of the maximum of partial sums of an Lq-mixingale array, and as corollary a strong law of large numbers (SLLN) for an Lq-mixingale sequence is shown by using the moment inequality. Finally, we prove a weak law of large numbers (WLLN) for an Lq-mixingale array without the condition of uniform integrability which is needed in Andrews [Andrews, D.W.K., 1988. Laws of large numbers for dependent non-identically distributed random variables. Econometric Theory 4, 458-467].

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