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

The limit theory of dependent sequences is one of the central issues for studying prob-ability, which has wide applications in reliability theory, multivariate statistical analysis, complex systems, financial risk theory and other fields.In this thesis, with the help of some techniques such as the continuity of probability, Markov inequality, maximal inequality, moment inequality, etc., we investigate some limit theorems for some kinds of dependent random variables. The specific results are as follows:Firstly, we obtain the large deviations for the partial sums of NA sequences, AANA sequences and NOD sequences under the conditions of∑i=1nE|Xi|P=O(n) and∑i=1n E|Xi|P=O(np).Secondly, we investigate the Hajek-Renyi-type inequality of NA sequences, AANA sequences in the case of1<p≤2and the Hajek-Renyi-type inequality of NOD sequences in the case of p=2.Thirdly, we discuss the strong law of large numbers and strong growth rate for NA sequences, AANA sequences and NOD sequences.