메뉴 건너뛰기




Volumn 37, Issue 4, 2005, Pages 1056-1074

Uniqueness criteria for continuous-time Markov chains with general transition structures

Author keywords

Birth death process; Downwardly skip free process; Markov branching process; Upwardly skip free process

Indexed keywords

DIFFERENTIAL EQUATIONS; LINEAR EQUATIONS; MATRIX ALGEBRA; PROBABILITY;

EID: 31944436197     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1134587753     Document Type: Article
Times cited : (20)

References (25)
  • 2
    • 0002227497 scopus 로고
    • The extinction time of a birth, death and catastrophe process and of a related diffusion model
    • Brockwell, P. J. (1985). The extinction time of a birth, death and catastrophe process and of a related diffusion model. Adv. Appl. Prob. 17, 42-52.
    • (1985) Adv. Appl. Prob. , vol.17 , pp. 42-52
    • Brockwell, P.J.1
  • 3
    • 0000229194 scopus 로고
    • The extinction time of a general birth and death process with catastrophes
    • Brockwell, P. J. (1986). The extinction time of a general birth and death process with catastrophes. J. Appl. Prob. 23, 851-858.
    • (1986) J. Appl. Prob. , vol.23 , pp. 851-858
    • Brockwell, P.J.1
  • 4
    • 0000934338 scopus 로고
    • Birth, immigration and catastrophe processes
    • Brockwell, P. J., Gani, J. and Resnick, S. I. (1982). Birth, immigration and catastrophe processes. Adv. Appl. Prob. 14, 709-731.
    • (1982) Adv. Appl. Prob. , vol.14 , pp. 709-731
    • Brockwell, P.J.1    Gani, J.2    Resnick, S.I.3
  • 5
    • 0037110123 scopus 로고    scopus 로고
    • Uniqueness and extinction properties of generalized Markov branching processes
    • Chen, A. Y. (2002). Uniqueness and extinction properties of generalized Markov branching processes. J. Math. Anal. Appl. 274, 482-494.
    • (2002) J. Math. Anal. Appl. , vol.274 , pp. 482-494
    • Chen, A.Y.1
  • 6
    • 0001143011 scopus 로고
    • Markov branching processes with instantaneous immigration
    • Chen, A. Y. and Renshaw, E. (1990). Markov branching processes with instantaneous immigration. Prob. Theory Relat. Fields 87, 204-240.
    • (1990) Prob. Theory Relat. Fields , vol.87 , pp. 204-240
    • Chen, A.Y.1    Renshaw, E.2
  • 7
    • 21144465641 scopus 로고
    • Existence and uniqueness criteria for conservative uni-instantaneous denumerable Markov processes
    • Chen, A. Y. and Renshaw, E. (1993). Existence and uniqueness criteria for conservative uni-instantaneous denumerable Markov processes. Prob. Theory Relat. Fields 94, 427-456.
    • (1993) Prob. Theory Relat. Fields , vol.94 , pp. 427-456
    • Chen, A.Y.1    Renshaw, E.2
  • 9
  • 10
    • 31944441733 scopus 로고
    • Uniqueness criterion for q-processes
    • Chen, M. F. and Zheng, X. G. (1983). Uniqueness criterion for q-processes. Sci. Sinica Ser. A 26, 11-24.
    • (1983) Sci. Sinica Ser. A , vol.26 , pp. 11-24
    • Chen, M.F.1    Zheng, X.G.2
  • 11
    • 0031082729 scopus 로고    scopus 로고
    • An extended class of time-continuous branching processes
    • Chen, R. R. (1997). An extended class of time-continuous branching processes. J. Appl. Prob. 34, 14-23.
    • (1997) J. Appl. Prob. , vol.34 , pp. 14-23
    • Chen, R.R.1
  • 12
    • 84966250746 scopus 로고
    • On the integro-differential equations of purely discontinuous Markoff processes
    • Feller, W. (1940). On the integro-differential equations of purely discontinuous Markoff processes. Trans. Amer. Math. Soc. 48, 488-515.
    • (1940) Trans. Amer. Math. Soc. , vol.48 , pp. 488-515
    • Feller, W.1
  • 13
    • 0013679254 scopus 로고    scopus 로고
    • Direct analytical methods for determining quasistationary distributions for continuous-time Markov chains
    • (Lecture Notes Statist. 114), eds C. C. Heyde et al., Springer, New York
    • Hart, A. G. and Pollett, P. K. (1996). Direct analytical methods for determining quasistationary distributions for continuous-time Markov chains. In Athens Conf. on Applied Probability and Time Series Analysis, Vol. 1 (Lecture Notes Statist. 114), eds C. C. Heyde et al., Springer, New York, pp. 116-126.
    • (1996) Athens Conf. on Applied Probability and Time Series Analysis , vol.1 , pp. 116-126
    • Hart, A.G.1    Pollett, P.K.2
  • 14
    • 0034702080 scopus 로고    scopus 로고
    • New methods for determining quasi-stationary distributions for Markov chains
    • Hart, A. G. and Pollett, P. K. (2000). New methods for determining quasi-stationary distributions for Markov chains. Math. Comput. Modelling 31, 143-150.
    • (2000) Math. Comput. Modelling , vol.31 , pp. 143-150
    • Hart, A.G.1    Pollett, P.K.2
  • 15
    • 1842794398 scopus 로고
    • The criterion for uniqueness of a Q-process
    • Hou, C. T. (1974). The criterion for uniqueness of a Q-process. Sci. Sinica 17, 141-159.
    • (1974) Sci. Sinica , vol.17 , pp. 141-159
    • Hou, C.T.1
  • 17
    • 0013505387 scopus 로고
    • The Markov branching-catastrophe process
    • Pakes, A. G. (1986). The Markov branching-catastrophe process. Stoch. Process. Appl. 23, 1-33.
    • (1986) Stoch. Process. Appl. , vol.23 , pp. 1-33
    • Pakes, A.G.1
  • 18
    • 1842643157 scopus 로고
    • Invariant measures for Q-processes when Q is not regular
    • Pollett, P. K. (1991). Invariant measures for Q-processes when Q is not regular. Adv. Appl. Prob. 23, 277-292.
    • (1991) Adv. Appl. Prob. , vol.23 , pp. 277-292
    • Pollett, P.K.1
  • 19
    • 0034759510 scopus 로고    scopus 로고
    • Quasi-stationarity in populations that are subject to large-scale mortality or emigration
    • Pollett, P. K. (2001). Quasi-stationarity in populations that are subject to large-scale mortality or emigration. Environ. Internat. 27, 231-236.
    • (2001) Environ. Internat. , vol.27 , pp. 231-236
    • Pollett, P.K.1
  • 20
    • 84976114139 scopus 로고
    • On the problem of establishing the existence of stationary distributions for continuous-time Markov chains
    • Pollett, P. K. and Taylor, P. G. (1993). On the problem of establishing the existence of stationary distributions for continuous-time Markov chains. Prob. Eng. Inf. Sci. 7, 529-543.
    • (1993) Prob. Eng. Inf. Sci. , vol.7 , pp. 529-543
    • Pollett, P.K.1    Taylor, P.G.2
  • 21
    • 0002855907 scopus 로고
    • Denumerable Markov processes and the associated contraction semigroups on l
    • Reuter, G. E. H. (1957). Denumerable Markov processes and the associated contraction semigroups on 1. Acta Math. 97, 1-46.
    • (1957) Acta Math. , vol.97 , pp. 1-46
    • Reuter, G.E.H.1
  • 22
    • 1842693569 scopus 로고
    • Denumerable Markov processes. IV. On C. T. Hou's uniqueness theorem for Q-semigroups
    • Reuter, G. E. H. (1976). Denumerable Markov processes. IV. On C. T. Hou's uniqueness theorem for Q-semigroups. Z. Wahrscheinlichkeitsth. 33, 309-315.
    • (1976) Z. Wahrscheinlichkeitsth. , vol.33 , pp. 309-315
    • Reuter, G.E.H.1
  • 24
    • 0347914931 scopus 로고
    • Generalized birth-death processes
    • (in Chinese)
    • Zhang, J. K. (1984). Generalized birth-death processes. Acta Math. Sinica 46, 241-259 (in Chinese).
    • (1984) Acta Math. Sinica , vol.46 , pp. 241-259
    • Zhang, J.K.1
  • 25
    • 0035533797 scopus 로고    scopus 로고
    • Strong ergodicity for single-birth processes
    • Zhang, Y. H. (2001). Strong ergodicity for single-birth processes. J. Appl. Prob. 38, 270-277.
    • (2001) J. Appl. Prob. , vol.38 , pp. 270-277
    • Zhang, Y.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.