Ergodicity of Quasi-birth and Death Processes(Ⅰ)  

作　　者：Zhen Ting HOU Xiao Hua LI 

机构地区：[1]School of Mathematics,Central South University [2]School of science,Beijing University of Posts and Telecommunications

出　　处：《Acta Mathematica Sinica,English Series》2007年第2期201-208,共8页数学学报（英文版）

基　　金：partially supported by NSFC(No.10171009);Research Fund for PhD Programs of MOE of China(No.20010533001);Research Fund for Educational Innovation for Doctorates of CSU(No.030602)

摘　　要：Quasi-birth and death processes with block tridiagonal matrices find many applications in various areas. Neuts gave the necessary and sufficient conditions for the ordinary ergodicity and found an expression of the stationary distribution for a class of quasi-birth and death processes. In this paper we obtain the explicit necessary and sufficient conditions for/-ergodicity and geometric ergodicity for the class of quasi-birth and death processes, and prove that they are not strongly ergodic. Keywords ergodicity, quasi-birth and death process.Quasi-birth and death processes with block tridiagonal matrices find many applications in various areas. Neuts gave the necessary and sufficient conditions for the ordinary ergodicity and found an expression of the stationary distribution for a class of quasi-birth and death processes. In this paper we obtain the explicit necessary and sufficient conditions for/-ergodicity and geometric ergodicity for the class of quasi-birth and death processes, and prove that they are not strongly ergodic. Keywords ergodicity, quasi-birth and death process.

关 键 词：ERGODICITY quasi-birth and death process Markov chain matrix geometric solutions 

分 类 号：O211.6[理学—概率论与数理统计]