The Properties Of Linear Birth And Death Process With Geometric Catastrophes

In this paper, we mainly study the linear birth and death process with geo-metric catastrophes, and mainly discuss the process about the recurrence, ergod-icity, stationary distribution, extinction times, probability of extinction and the quasi-stationary distribution.The first chapter is the introduction of the paper, which mainly introduces the research significance, research status and the main work of the linear birth and death process with geometric catastrophes.The second chapter is about the basic theory of the continuous time Markov chain, the sinle birth Q-process and the linear birth and death process with geo-metric catastrophes.The third chapter, we mainly study the recurrence, ergodicity, stationary dis-tribution in the irreducible linear birth and death process with geometric catas-trophes. We get the necessary and sufficient conditions of the recurrence and an explicit criterion for the recurrence of the process is obtained.In the fourth chapter, we study the mean extinction times and probability of extinction in the linear birth and death process with geometric catastrophes and absorbing state 0. we conclude the necessary and sufficient conditions for this model.In the fifth chapter, we study the existence of quasi-stationary distribution in the linear birth and death process with geometric catastrophes and absorbing state O.we get the necessary and sufficient conditions for this model.