Conditions For Quasi-Stationary Distribution Of Birth And Death Processes With Killing

The process of further development on the basis of the process of birth and death is the process of birth and death with killing.It is a special kind of Markov process and has important practical significance.The quasi-stationary distribution of a class of birth and death processes with killing is studied in this paper.On the basis of previous studies,it is made that the process of birth and death with killing is”dead”rather than”killed”in the state of 1,that is,the death rate of the process in the state of（9₁>0,the killing rate of the process in the state of6）₁=0,and the rate at which the process gets killed at state 2,3...is6)₂,6)₃...≥0.Based on this,a special?₉)is defined to define a dual existence process.By studying this dual birth and death process,the existence condition of the quasi-stationary distribution of the birth and death process with killing is obtained.In the first chapter,we mainly discuss from three aspects:research back-ground and significance,research history and current situation,and the main work of this paper.In the second chapter,we focus on the Markov chain,the birth and death process and some basic theories of quasi-stationary distribution.In the third chapter,we mainly introduce the basic model of the birth and death process of killing,the process of dual birth and death,and the quasi-stationary distribution of the birth and death process of such killing.In the fourth chapter,we mainly use two special examples of killing to verify the conclusion of Chapter 3.Finally,we summarize the main work and conclusions of this paper.