The Related Problem Research Of Quasi-Stationary Distribution

In this paper,we study a class of processes with catastrophes,verify an impor-tant condition of the theorem,there is the quasi-stationary distribution and given equivalent lemma of the important condition for the quasi-stationary distribution and a series coefficients and function.In the first chapter,we mainly introduce the background,significance,history,current situation and primarily conclusion.The second chapter is mainly talk about time-continuous Markov chain,birth and death process and quasi-stationary distribution theories which this word will be used.The third chapter verify an important result of existence condition of quasi-stationary distribution and it is proved by finding a specific model with equivalent lemma.Finally,we get the properties of Q matrix,such as extinction with proba-bility 1 and the average extinction time is infinite so on.The forth chapter conclude the paper,include all the conclusions and outlook the question not be solved.