Ergodicity of Quasi-birth and Death Processes (I)

Citation
Hou," Zhen Ting",li," Xiao Hua, Ergodicity of Quasi-birth and Death Processes (I), Acta mathematica Sinica. English series (Print) , 23(2), 2007, pp. 201-208
ISSN journal
14398516
Volume
23
Issue
2
Year of publication
2007
Pages
201 - 208
Database
ACNP
SICI code
Abstract
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 l-ergodicity and geometric ergodicity for the class of quasi-birth and death processes, and prove that they are not strongly ergodic.