The Monotonicity For A Class Markov Chains With A Catastrophe

Today to study the distribution of the quasi stationary markov process is an important branch of theoretical research in a random process especially for random monotone process。it has a wide range of applications In biology, physics, chemistry and other ?elds, especially in the research of life science it has made outstanding contributions. Our paper is mainly to study quasi stationary distribution for a general birth,death and catastrophe markov process in the case of linear.The ?rst chapter is the introduction part of this paper, mainly introduced the research background, research status quo of markov process as well as in this article we study the related conclusion.The second chapter is the preliminary knowledge of markov process, this paper introduces the continuous time markov process, random monotone markov process and the basic theory of quasi stationary distribution.The third chapter we learn a model of a general birth,death and catastrophe markov process. this chapter we have summarized the related work of other scholars do with this model,on the basis of their work of the model,we have given two sufficient conditions and a sufficient and necessary condition of the Q matrix monotonous.The fourth chapter we thinked about the linear of the transfer rate, we have proved its Q matrix is monotonous, and proved that the process has only one Quasi stationary distribution.