Equivalent Theorems For Average Extinction Time Of Stochastic Monotone Markov Processes Was Limited And Its Application

This paper mainly studied the stochastically monotonous Markov processes.As we all know when the Markov process was stochastically monotonous,so its dual process must exist.Then we obtained the equivalent theorem,namely: any continuous-time Markov chains,as long as it satisfied irreducibility,regularity,stochastic monotonicity,then that the average extinction time of this process was limited was equivalent to that this process‘s dual process was transient.Secondly,we used the generalised birth and death process to show that the equivalence theorem was right;then this paper studied the generalised Markov branching process,and by using the equivalence theorem,we obtained that the necessary and sufficient condition about that the dual process of the generalised Markov branching process was transient.Finally,the equivalence theorem was applied to the linear birth and death process with binomially distributed catastrophes,and we obtained that the average extinction time was limited was equivalent to whose dual process was transient?...