The Conditions Of A Unique Quasi-stationary Distribution For Markov Processes

In this paper, the object studied is a Markov process X(t) on the nonnegative integers E=C U{0}, where C={1,2,...} is an irreducible class and 0 an absorbing state. Suppose X(t) is inevitably absorbed in the state 0, and the corresponding Q-matrix is conserved. By studying quasi-stationary distributions for X(t), we get a necessary condition and also received a series of propositions which are equivalent to the necessary conditions.In the first chapter, we introduce the background, history and current status of Markov process the stationary distribution, and also present some basics of Markov processes. Finally, we introduce concepts related quasi-stationary distributions and μ-invariant measure.In the second chapter, we introduce three theorems and two examples. In the first theorem, if there exists a unique quasi stationary distribution for the Markov process X(t), and this distribution absorb all the all initial distributions snpi∈C EiiT<∞. The second theorem contains five propositions which are equiv-alent to supi∈C EiT<∞: (v) There exists a bounded non-negative solution of the system In the third theorem, if pi incEiT< infty, then the decay parameter λC> 0.In the third chapter, we summarize the conclusions and present some of the relevant issues to be solved.