Coefficients of ergodicity for imprecise Markov chains

ISIPTA 2009 - Proceedings of the 6th International Symposium on Imprecise Probability: Theories and Applications

Volumn , Issue , 2009, Pages 377-386

  Škulj, Damjan ^a   Hable, Robert ^b  

^a UNIVERSITY OF LJUBLJANA   (Slovenia)

^b UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

Coefficient of ergodicity; Imprecise markov chain; Lower expectation; Markov chain; Upper expectation

Indexed keywords

ERGODICITY; IMPRECISE MARKOV CHAINS; IMPRECISE PROBABILITIES; LOWER EXPECTATION; METRIC SPACES; UPPER EXPECTATION;

PROBABILISTIC LOGICS; PROBABILITY;

MARKOV PROCESSES;

EID: 84858798412     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (21)

1. G. Beer. Topologies on closed and closed convex sets. Kluwer Academic Publishers, Dordrecht, 1993.
2. G. de Cooman, F. Hermans, and E. Quaeghebeur. Imprecise Markov chains and their limit behaviour. Probability in the Engineering and Informational Sciences, 2009.
3. R.L. Dobrushin. Central limit theorem for nonstationary Markov chains, I, II. Theory of Probability and its Applications, 1(4):329-383, 1956.
4. N. Dunford and J.T. Schwartz. Linear Operators. Part I: General Theory. Wiley, New York, 1988.
5. Ky Fan. Minimax theorems. Proceedings of the National Academy of Sciences of the United States of America, 39:42-47, 1953.
6. R. Hable. Data-based decisions under complex uncertainty. PhD thesis, Ludwig-Maximilians- Universität (LMU) Munich, 2009.
7. D. Harmanec. Generalizing Markov decision processes to imprecise probabilities. Journal of Statistical Planning and Inference, 105:199-213, 2002.
8. D.J. Hartfiel. Markov Set-Chains. Springer- Verlag, Berlin, 1998.
9. D.J. Hartfiel and E. Seneta. On the theory of Markov set-chains. Advances in Applied Probability, 26(4):947-964, 1994.
10. H. Itoh and K. Nakamura. Partially observable Markov decision processes with imprecise parameters. Artificial Intelligence, 171(8-9):453-490, 2007.
11. I. Kozine and L.V. Utkin. Interval-valued finite Markov chains. Reliable Computing, 8(2):97-113, 2002.
12. A. Nilim and L. El Ghaoui. Robust control of Markov decision processes with uncertain transition matrices. Operations Research, 53:780-798, 2005.
13. A. Paz. Ergodic theorems for infinite probabilistic tables. Annals of Mathematical Statistics, 41(2):539-550, 1970.
14. J.K. Satia and R.E. Lave. Markovian decision processes with uncertain transition probabilities. Operations Research, 21(3):728-740, 1973.
15. E. Seneta. Coefficients of ergodicity - structure and applications. Advances in Applied Probability, 11(2):270-271, 1979.
16. D. Škulj. Finite discrete time Markov chains with interval probabilities. In J. Lawry, E. Miranda, A. Bugaŕin, S. Li, M. A. Gil, P. Grzegorzewski, and O. Hryniewicz, editors, SMPS, volume 37 of Advances in Soft Computing, pages 299-306. Springer, 2006.
17. D. Škulj. Regular finite Markov chains with interval probabilities. In G. de Cooman, M. Zaffalon, and J. Vejnarov́a, editors, ISIPTA'07 - Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications, pages 405-413. SIPTA, 2007.
18. P. Walley. Statistical reasoning with imprecise probabilities. Chapman and Hall, London, New York, 1991.
19. P. Walley. Towards a unified theory of imprecise probability. International Journal of Approximate Reasoning, 24:125-148, 2000.
20. K. Weichselberger. Elementare Grundbegriffe einer allgemeineren Wahrscheinlichkeitsrechnung. I: Intervallwahrscheinlichkeit als umfassendes Konzept. Physica-Verlag, Heidelberg, 2001.
21. C.C. White and H.K. Eldeib. Markov decision processes with imprecise transition probabilities. Operations Research, 42(4):739-749, 1994.