Study On The Related Properties Of A Class Of Birth And Death Processes With Uniform Catastrophes

Based on the model of the birth and death process with uniform catastrophes proposed by P.J.Brockwell,this paper focuses on the extinction probability,mean extinction time and decay parameter.The first chapter describes the development background and current situation of the birth and death process with catastrophe and the innovation points of the birth and death process with uniform catastrophe studied in this paper.The second chapter describes the theories – markov process,birth and death process,single birth process,quasi-stationary distribution and decay parameter.The third chapter introduces the model 1,Secondly,the sufficient and necessary conditions of model 1 with probability 1 extinction are solved by simple method,and the sufficient conditions of mean extinction time less than infinity are discussed.The fourth chapter is the second conclusion of model 1,which focuses on obtaining a lower bound of the decay parameter by using the stochastic monotone comparablity of the birth and death process-matrix,and obtaining an upper bound by using the decay parameter theorem.In fifth chapter,we first introduce the basic model of model 2,and then calculate the necessary and sufficient conditions for the model with probability1 extinction and mean extinction time less than infinite by using the related properties of single birth process,and obtain the specific expressions of extinction probability and mean extinction time.