Time-homogeneous birth-death processes with probability intervals and absorbing state

Journal of Statistical Theory and Practice

Volumn 3, Issue 1, 2009, Pages 103-118

  Crossman, Richard J ^a   Coolen Schrijner, Pauline ^a   Coolen, Frank P A ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Absorbing state; Birth death process; Interval probability; Limiting conditional distribution; Quasi stationary distribution; Time homogeneity

Indexed keywords

EID: 85008826198     PISSN: 15598608     EISSN: 15598616     Source Type: Journal    
DOI: 10.1080/15598608.2009.10411914     Document Type: Article

References (18)

1. Avrachenkov, K., Sanchez, E., 2002. Fuzzy Markov chains. Fuzzy Optimisation and Decision Making, 1, 143–159.
2. Darroch, J., Seneta, E., 1965. On the quasi-stationary distributions in absorbing discrete-time finite Markov chains. Journal of Applied Probability, 2, 88–100.
3. de Cooman, G., Quaeghebeur, E., Miranda, E., 2008. Imprecise Markov chains and their limit behaviour. Pre-print at arXiv.org, arXiv:0801.0980.
4. Feller, W., 1950. An Introduction to Probability Theory and its Applications, Volume 1, 3rd edition, Wiley, New York.
5. Kijima, M., 1997. Markov Processes for Stochastic Modelling. Chapman & Hall, London.
6. Kozine, I., Utkin, L., 2002. Interval-valued finite Markov chains. Reliable Computing, 8, 97–113.
7. Pakes, A., 1987. Limit theorems for the population size of a birth and death process allowing catastrophes. Journal of Mathematical Biology, 25, 307–325.
8. Parsons, R., Pollett, P., 1987. Quasistationary distributions for auto-catalytic reactions. Journal of Statistical Physics, 46, 249–254.
9. Schweitzer, P., 1968. Perturbation theory and finite Markov chains. Journal of Applied Probability, 5, 401–413.
10. van Doorn, E., Schrijner, P., 1995a. Geometric ergodicity and quasi-stationarity in discrete-time birth-death processes. Journal of the Australian Mathematical Society Series B, 37, 121–144.
11. van Doorn, E., Schrijner, P., 1995b. Ratio limits and limiting conditional distributions for discrete-time birth-death processes. Journal of Mathematical Analysis and Applications, 190, 263–284.
12. Skulj, D., 2006. Finite discrete time Markov chains with interval probabilities. In Soft Methods for Integrated Uncertainty Modelling, Lawry, J., Miranda, E., Bugarin, A., Li, S., Gil, M.A., Grzegorzewski, P., Hryniewicz, O. (editors), 299–306. Springer, Berlin.
13. Sˇkulj, D., 2007. Regular finiteMarkov chains with interval probabilities. In Proceedings of 5th International Symposium on Imprecise Probabilities and Their Applications, de Cooman, G., Vejnarová, J., Zaffalon, M. (editors), 406–413. Prague, Czech Republic.
14. Walley, P., 1991. Statistical Reasoning with Imprecise Probabilities. Chapman & Hall, London.
15. Weichselberger, K., 2000. The theory of interval-probability as a unifying concept for uncertainty. International Journal of Approximate Reasoning, 24, 149–170.
16. Weichselberger, K., 2001. Elementare Grundbegriffe einer allgemeineren Wahrscheinlichkeitsrechnung I. Intervallwahrscheinlichkeit als umfassendes Konzept. Physika: Heidelberg.
17. Wise, J., 1962. The relationship between the mean and variance of a stationary birth-death process, and its economic application. Biometrika, 49, 253–255.
18. Yaglom, A., 1947. Certain limit theorems of the theory of branching stochastic processes (in Russian). Dokl. Akad. Nauk SSSR, 56, 795–798.