Large Deviations And Strong Law Of Large Numbers For Some Dependent Random Variable Sequences

The study of the limit theory of dependent random variable sequences is the inevitability of researching the probability limit theory.Based on the large deviations of special dependent random variable sequences,this article further explores their limit results-different forms of the strong law of large numbers.Firstly,in this paper we present some large deviations for martingale difference sequence,?-mixing sequence,p-order M-Z type random variable sequence and NOD sequence under the condition of(?)E|Xi|p=O(n).Secondly,by the large deviation of AANA sequence,combing strong law of large numbers for random sequences,we establish the Brunk-Prokhorov type strong law of large numbers for AANA random variable sequences when p meets different conditions.At the same time,we derive the Brunk-Prokhorov type strong law of large numbers for NA sequence which is a special sequence of AANA sequence.Finally,we obtain the strong law of large numbers for weighted sums of m-AANA sequences under different conditions by truncating method.