Imprecise Markov chains with absorption

International Journal of Approximate Reasoning

Volumn 51, Issue 9, 2010, Pages 1085-1099

  Crossman, R J ^a   Skulj D ^b  

^a DURHAM UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF LJUBLJANA   (Slovenia)

Author keywords

Interval probabilities; Markov chains; Quasi stationary distributions

Indexed keywords

CHAINS; PROBABILITY; PROBABILITY DISTRIBUTIONS; UNCERTAINTY ANALYSIS;

ABSORBING STATE; CLASSICAL THEORY; CONDITIONAL PROBABILITIES; IMPRECISE MARKOV CHAINS; INTERVAL PROBABILITY; QUASI-STATIONARY DISTRIBUTION; REGULARITY CONDITION; UNCERTAIN PARAMETERS;

MARKOV PROCESSES;

EID: 84862687234     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2010.08.008     Document Type: Article

References (17)

1. G. Beer, Topologies on Closed and Closed Convex Sets, Kluwer Academic Publishers, 1993.
2. G. De Cooman, E. Quaeghebeur, E. Miranda, Imprecise Markov chains and their limit behaviour, Probability in the Engineering and Informational Sciences 23 (2009) 597-635.
3. R.J. Crossman, P. Coolen-Schrijner, F.P.A. Coolen, Time homogeneous birth-death processes with probability intervals and absorbing state, Journal of Statistical Theory and Practice 3 (2009) 103-118.
4. R.J. Crossman, P. Coolen-Schrijner, F.P.A. Coolen, Imprecise Markov chains with an absorbing state, in: T. Augustin, F.P.A. Coolen, S. Moral, M. Troffaes (Eds.), Proceedings of the Sixth International Symposium on Imprecise Probabilities: Theory and Applications, Durham, UK, 2009, pp. 119-128.
5. R.J. Crossman, Limiting Conditional Distributions: Imprecision and Relation to the Hazard Rate, Ph.D. Thesis, Durham University, UK, 2009.
6. J.N. Darroch, E. Seneta, On quasi-stationary distributions in absorbing discrete-time finite Markov chains, Journal of Applied Probability 2 (1965) 88-100.
7. D.J. Hartfiel, Markov Set-Chains, Springer-Verlag, 1998.
8. I.O. Kozine, L.V. Utkin, Interval-valued finite Markov chains, Reliable Computing 8 (2002) 97-113. (Pubitemid 34254805)
9. P. Olofsson, Probability Statistics and Stochastic Processes, Wiley, 2005.
10. E. Seneta, Non-Negative Matrices and Markov Chains, Springer-Verlag, 1981.
11. D. Škulj, Finite Discrete Time Markov Chains with Interval Probabilities, Soft Methods for Integrated Uncertainty Modelling, Springer, 2006.
12. D. Škulj, R. Hable, Coefficients of ergodicity for imprecise Markov chains, in: T. Augustin, F.P.A. Coolen, S. Moral. M. Troffaes (Eds.), Proceedings of the Sixth International Symposium on Imprecise Probabilities: Theory and Applications, Durham, UK, 2009, pp. 119-128.
13. D. Škulj, Discrete time Markov chains with interval probabilities, International Journal of Approximate Reasoning 50 (2009) 1314-1329.
14. L.A. Steen, Counterexamples in Topology, Springer-Verlag, 1970.
15. H.C. Tijms, A First Course in Stochastic Models, Wiley, 2003.
16. P. Walley, Statistical Reasoning with Imprecise Probabilities, Chapman & Hall, 1991.
17. K. Weichselberger, The theory of interval-probability as a unifying concept for uncertainty, International Journal of Approximate Reasoning 24 (2000) 149-170. (Pubitemid 34200944)