The Studies Of Covergence Properties And Strong Law Of Large Numbers For AANA Sequence

In this paper, we investigated the properties of AANA sequence of random variables, which are weaker than NA random variables. Based on the maximal inequality of AANA sequence, we firstly obtain the Khintchine-Kolmogorov convergence for AANA sequence. As an application, we study the three series theorem for AANA random variables. Our results of Khintchine-Kolmogorov convergence and three series theorem for AANA random variables generalize the corresponding ones of independent random variables and NA random variables.Meanwhile, based on the maximal inequality of AANA random variables, we get the strong law of large numbers, strong growth rate and the integrability of supremum for AANA random variables.