Discussions Of Some Issues On Generalized Convolution Equivalent Distribution

In the distribution theory, the convolution equivalent distribution not only has become a hot research content among the scholars, but also has general applications in queueing system, branching process and risk theory,so they have been paid more and more attention. It is well known that the study of distributions’ expansion and the research on their properties have become one of the research directions. The closure of the convolution and convolution roots have become one of the important content of research. And the research of Kesten’s Bound is from the aspects of analysis and probability. This paper mainly discusses well properties of the generalized convolution equivalent distribution class in the whole space, and simplifies and generalizes some relevant properties.The first chapter, introduction, mainly introduces some common distributions,the concepts of two new distribution class, existing results and the writing motivation briefly.The second chapter discusses the generalized convolution equivalent distribution,especially the closure of the convolution roots in whole space, in section 2.2. In addition, discussion on some properties of the integrated tail distribution is also given.The third chapter is another key. From the aspect of Kesten’s bound, and twodifferent perspectives of analysis and probability.We prove theorem 3.1, which makes us having a more comprehensive understanding on its properties.