Rough Large Deviations For Sums Of Negatively Associated Random Variables

It is well known that rough large deviations theory is to study the logarithmic tailasymptotics. It have wide and important applications to many fields such as queueingtheory, risk theory and so on. In the early researches, the objects were supposed to beindependent identically distributed random variables. However, in the practical applica-tions, there may exist some dependent among these random variables, and they may not beindependent, and may not be common distributions. In this paper, we will regard roughlarge deviations for sums of negatively associated random variables. In Chapter 2, wediscuss rough large deviations for one kinds negatively associated random variables withdifferent distributions and negatively associated random variables with common two-sidedistributions. In Chapter 3, we also have some results about large deviations for randomvariables with common dominatedly varying tails. Our results are improve some resultsof Hu and Nyrhinen(2004) and Yang, Wang, Wang and Cui(2006).