Study On The Related Properties Of Birth And Death Processes With Killing

Starting from the birth and death process,this paper summarizes the con-ditions for the existence of quasi-stationary distribution().Then we con-sider birth and death process with killing{(3(),?0},whose state space is={0}?,={1,2,···},using some transformation,the killing rate6)₄),4)?is eliminated of birth and death process with killing,and the birth and death pro-cess with only birth rate(7₄)and death rate(9₄)is obtained.Then we study the relationship between the two processes,including the relationship between the size of the decay parameter,the relationship between the transfer function and the quasi-stationary distribution,extend the existing relevant conclusions of birth and death process to birth and death process with killing,so as to complete the study on the related properties of the birth and death process with killing.Final-ly,the conclusion is applied to relevant examples of the birth and death process with killing.