Linear Birth And Death Process With Immigration And Killing

In this paper, we mainly study the linear birth and death process with immigra-tion and killing, and mainly discuss the conditions about the extinction probability in a linear birth and death process with immigration and killing and the decay parameter and the problem of the quasi-stationary distribution of the process.The first chapter is the introduction of the paper, which mainly introduces the research background, research status and the main work of the Markov process.The second chapter is about the basic theory of the continuous time Markov chain, the birth death process with killing and the quasi stationary distribution.The third chapter,we mainly study the extinction probability and decay pa-rameters in a birth and death process with immigration and immigration. We get the necessary and sufficient conditions of the extinction probability and the specific form of the decay parameters.In the fourth chapter, we study the domain of attraction of the quasi-stationary distribution for the linear birth and death process with immigration and killing. We prove that the linear birth-death processes with linear killing has precisely one quasi-stationary distribution which is a binomial distribution. And any initial distribution is in the domain of attraction of the unique quasi-stationary distribution.