Conditions For The Existence Of Quasi-Stationary Distributions For Birth-Death Processes With Killing

In this paper,we consider conditions for the existence of quasi-stationary distributions for birth-death processes with killing,a method to study conditions for the existence of quasi-stationary distributions for birth-death processes with killing,through the proper transformation we will take to birth-death processes with killing into the birth-death processes,through the study of the conditions for the existence of quasi-stationary distributions for birth-death process,we will get the conditions for the existence of quasi-stationary distributions for birth-death processes with killing.The first chapter is the introduction of the paper,which mainly introduces the research background,the present research status and the main work of the Markov process.The second chapter is the preliminary knowledge part,mainly introducing the related concepts and related theories of continuous time Markov chains,birth-death processes and quasi-stationary distributions.The third chapter is the core part of this paper,we mainly study the condi-tions for the existence of quasi-stationary distributions for birth-death processes with killing,sufficient conditions are obtained for the decay parameter ?>0 and conditions for the existence of quasi-stationary distributions for birth-death processes with killing,and give some examples.The fourth chapter is a summary of the main results of this paper.