Limiting conditional distributions for birth-death processes

Advances in Applied Probability

Volumn 29, Issue 1, 1997, Pages 185-204

  Kijima, M ^a   Nair, M G ^b   Pollett, P K ^c   Van Doorn, E A ^d  

^a UNIVERSITY OF TSUKUBA   (Japan)

^b CURTIN UNIVERSITY   (Australia)

^c UNIVERSITY OF QUEENSLAND   (Australia)

^d UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Invariant measures; Quasi stationary distributions

Indexed keywords

EID: 0001133302     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800027841     Document Type: Article

References (17)

1. ANDERSON, W. J. (1991) Continuous-Time Markov Chains - An Applications-Oriented Approach. Springer, New York.
2. CHIHARA, T. S. (1978) An Introduction to Orthogonal Polynomials. Gordon and Breach, New York.
3. ELMES, S., POLLETT, P. K. AND WALKER, D. M. (1994) Further results on the relationship between μ-invariant measures and quasistationary distributions for continuous-time Markov chains. Statistics Research Report. University of Queensland.
4. FERRARI, P. A., KESTEN, H., MARTÍNEZ, S. AND PICCO, P. (1995) Existence of quasi-stationary distributions. A renewal dynamical approach. Ann. Prob. 23, 501-521.
5. FLASPOHLER, D. C. (1974) Quasi-stationary distributions for absorbing continuous-time denumerable Markov chains. Ann. Inst. Statist. Math. 26, 351-356.
6. KARLIN, S. AND MCGREGOR, J. L. (1957) The differential equations of birth-and-death processes, and the Stieltjes moment problem. Trans. Amer. Math. Soc. 85, 489-546.
7. KARLIN, S. AND MCGREGOR, J. L. (1957) The classification of birth and death processes. Trans. Amer. Math. Soc. 86, 366-400.
8. KIJIMA, M. AND SENETA, E. (1991) Some results for quasi-stationary distributions of birth-death processes. J. Appl. Prob. 28, 503-511.
9. KIJIMA, M. AND VAN DOORN, E. A. (1995) Weighted sums of orthogonal polynomials with positive zeros. J. Comput. Appl. Math. 65, 195-206.
10. NAIR, M. G. AND POLLETT, P. K. (1993) On the relationship between μ-invariant measures and quasistationary distributions for continuous-time Markov chains. Adv. Appl. Prob. 25, 82-102.
11. PAKES, A. G. (1995) Quasi-stationary laws for Markov processes: examples of an always proximate absorbing state. Adv. Appl. Prob. 27, 120-145.
12. POLLETT, P. K. (1988) Reversibility, invariance and μ-invariance. Adv. Appl. Prob. 20, 600-621.
13. VAN DOORN, E. A. (1985) Conditions for exponential ergodicity and bounds for the decay parameter of a birth-death process. Adv. Appl. Prob. 17, 514-530.
14. VAN DOORN, E. A. (1986) On orthogonal polynomials with positive zeros and the associated kernel polynomials. J. Math. Anal. Appl. 113, 441-450.
15. VAN DOORN, E. A. (1987) The indeterminate rate problem for birth-death processes. Pacific J. Math. 130, 379-393.
16. VAN DOORN, E. A. (1991) Quasi-stationary distributions and convergence to quasi-stationarity of birth-death processes. Adv. Appl. Prob. 23, 683-700.
17. VERE-JONES, D. (1969) Some limit theorems for evanescent processes. Austral. J. Statist. 11, 67-78.