Large Deviations For The Partial Sums And Random Sums Of NOD Sequences

Precise large deviations as the center content of actuarial mathematics has grad-ually become a hot topic of the actuarial community, it plays a very important role in describing extremal events. In risk theory, the heavy-tailed model is usually used to describe the large claims. Their insurance and financial mathematics played an important role. As the actual needs of the relevant random variables Precise large deviations studies have caused concern Since Nagaev, and Nagaev, SV for the first time established independent and identically distributed of heavy tailed random variables and the theory of large deviations for the fine since the research in this area has been very hot, and there are a lot of research results.Joag-Dev and Proschan in1983and the introduction of a NOD sequence of concept, but on the NOD series of articles is not a lot. This paper studies the NOD and with random sequences and the large deviations. Paper consists of three parts:The first part introduces some common heavy tailed distributions, and the corresponding given its simple nature, then the large deviations of the fine research background and have the results of the review, the last on this paper to study the contents of a simple summary.The second part of the first introduction of a NOD sequence of concept, and gives some of its simple nature, then consider the family of the εRV heavy tailed distributions, and has been on the same family of εRV distribution distribution NOD sequences and large deviation results, the last on this basis and given a random case of large deviation results.The third part of the basis in the second part of the conditions we will be weakened further promote NOD and with random sequences and the large deviation results are obtained in different distribution of D distributions and NOD and with random sequences and the large deviation results.