Study On The Related Properties Of Birth And Death Process With Uniform Catastrophes

For the related model of the birth and death processes with uniform catastro-phes, we are mainly devoted to discuss the problems about the stochastic mono-tonicity, duality, extinction probability and the mean extinction time.The first chapter mainly introduces the research background and research status of the birth and death processes with uniform catastrophes, and the main conclusions that I have come to in this paper.In the second chapter, some relative basic theories of the continuous time Markov chains, the birth and death processes and the quasi-stationary distribu-tions are introduced.The third chapter and the fourth chapter are the core parts of the paper, we mainly proof the the stochastic monotonicity of the birth and death processes with uniform catastrophes and the dual matrix is given. Next, we get the sufficient con-ditions for the extinction probability and the mean extinction time of the model we discuss in this paper.The fifth chapter is the summary and prospect. For the decay parameters and the quasi-stationary distribution of related models of the process, this paper did not get a good conclusion. Hoping to gather everyone's wisdom, we can carry out more in-depth study.