TY - JOUR
T1 - Quasi-stationarity and quasi-ergodicity of general Markov processes
AU - Zhang, Jun Fei
AU - Li, Shou Mei
AU - Song, Ren Ming
N1 - Funding Information:
Acknowledgements This research was supported by National Natural Science Foundation of China (Grant No. 11171010) and Beijing Natural Science Foundation (Grant No. 1112001). The first author would like to thank the support of the China Scholarship Council. The third author would like to thank the support from Beijing Hai Ju Project and Beijing University of Technology. The authors thank the referees for helpful comments on the first version of this paper.
PY - 2014/10
Y1 - 2014/10
N2 - In this paper, we study the quasi-stationarity and quasi-ergodicity of general Markov processes. We show, among other things, that if X is a standard Markov process admitting a dual with respect to a finite measure m and if X admits a strictly positive continuous transition density p(t, x, y) (with respect to m) which is bounded in (x, y) for every t > 0, then X has a unique quasi-stationary distribution and a unique quasi-ergodic distribution. We also present several classes of Markov processes satisfying the above conditions.
AB - In this paper, we study the quasi-stationarity and quasi-ergodicity of general Markov processes. We show, among other things, that if X is a standard Markov process admitting a dual with respect to a finite measure m and if X admits a strictly positive continuous transition density p(t, x, y) (with respect to m) which is bounded in (x, y) for every t > 0, then X has a unique quasi-stationary distribution and a unique quasi-ergodic distribution. We also present several classes of Markov processes satisfying the above conditions.
KW - Markov processes
KW - mean ratio quasi-stationary distributions
KW - quasi-stationary distributions
KW - quasiergodicity distributions
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U2 - 10.1007/s11425-014-4835-x
DO - 10.1007/s11425-014-4835-x
M3 - Article
AN - SCOPUS:84906088197
SN - 1674-7283
VL - 57
SP - 2013
EP - 2024
JO - Science China Mathematics
JF - Science China Mathematics
IS - 10
ER -