Entropy maximization for Markov and semi-Markov processes

Methodology and Computing in Applied Probability

Volumn 6, Issue 1, 2004, Pages 109-127

  Girardin, Valerie ^a  

^a UNIVERSITÉ DE CAEN   (France)

Author keywords

Jump Markov processes; Markov chains; Maximum of entropy; Reliability; semi Markov processes

Indexed keywords

EID: 1642399425     PISSN: 13875841     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:MCAP.0000012418.88825.18     Document Type: Review

References (27)

1. M. Bad Dumitrescu, "Some informational properties of Markov pure jump processes," Cas. Pestovani Mat. vol. 113pp. 429-434, 1988.
2. C. Balcǎu, "L'optimisation de l'entropie des chaînes de Markov," Bull. Math. Soc. Math. Roumanie vol. 37 pp. 21-41, 1993.
3. T. Berger, Rate Distortion Theory, Prentice Hall: Englewood Cliffs, 1971.
4. R. J. Boucherie and E. A. van Doorn, "Uniformization for 1-Positive Markov Chains," Commun. in Stat.: Stoch Mod. vol. 14 pp. 171-186, 1998.
5. L. Breiman, "The individual ergodic theorem of information theory," Ann. Math. Stat. vol. 28 pp. 809-811, 1957.
6. L. Breiman, "Correction to: the individual ergodic theorem of information theory," Ann. Math. Stat. vol. 31 pp. 809-810, 1960.
7. L. Cover and J. Thomas, Elements of Information Theory, Wiley series in telecommunications: New-York, 1991.
8. Y. Gerchak, "Maximal entropy of Markov chains with common steady-states probabilities," J. Oper. Res. Soc. vol. 32 pp. 233-234, 1981.
9. V. Girardin and N. Limnios, Probabilités en vue des Applications, Vuibert: Paris, 2001.
10. V. Girardin and N. Limnios, "On the entropy for semi-Markov processes," J. Applied Probab vol. 40 pp. 1060-1068, 2003.
11. E. Grandori Guagenti and C. Molina, "Semi-Markov processes in seismic risk analysis," In Janssen (ed.), Semi-Markov Models: Theory and Applications, Plenum: New York, pp. 487-506, 1986.
12. T. Hohöldt and J. Justesen, "Maxentropic Markov chains," IEEE Trans. Inf. Theory vol. 30 pp. 665-667, 1984.
13. R. A. Howard, Dynamic Probabilistic Systems, vol. I: Markov Models, vol. II: Semi-Markov and Decision Processes, Series in Decision and Control, John Wiley & Sons: New York, 1971.
14. J. N. Kapur, Maximum Entropy Models in Sciences and Engineering, John Wiley: New York, 1989.
15. D. Kazakos, "Robust noiseless source coding through a game theoretic approach," IEEE Trans. Inf. Theory vol. 29 pp. 576-583, 1983.
16. J. Kieffer, "A simple proof of the Moy-Perez generalization of the Shannon-McMillan theorem," Pacific J. Math. vol. 51 pp. 203-206, 1974.
17. N. Limnios and O. Oprişan, Semi-Markov Processes and Reliability, Birkhauser: Boston, 2001.
18. M. McMillan, "The basic theorems of information theory," Ann. Math. Stat. vol. 24 pp. 196-219, 1953.
19. M. Merzéréaud, Entropie et processus de Markov: Un critère de choix du processus randomisé T. E. R., Université de Caen, 2002.
20. G. R. Mohtashami Borzadaran "Characterization of Pearsonian and bilateral power series distribution via maximum entropies," In A. Mohammad-Djafari (ed.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, AIPCP, pp. 145-150, 2001.
21. P. Moran, "Entropy, Markov processes and Boltzmann's H-theorem," Proc. Camb. Philos. Soc. vol. 57 pp. 833-842, 1961.
22. A. Perez, "Extensions of Shannon-McMillan's limit theorem to more general stochastic processes," Inf. Theory, Stat. Decision Functions, Random Processes pp. 545-574, 1964.
23. D. Politis, "Nonparametric maximum entropy," IEEE Trans. Inf. Theory vol. 39 pp. 1409-1413, 1993.
24. N. Ravichandran, Stochastic Methods in Reliability Theory, John Wiley: New York, 1990.
25. P. Rocchi, "Boltzmann-like entropy in reliability theory," Entropy vol. 4 pp. 142-150, 2002.
26. C. Shannon, "A mathematical theory of communication," Bell Syst., Techn. J. vol. 27 pp. 379-423, 623-656, 1948.
27. F. Spitzer, "A variational characterization of finite Markov chains," Ann. Math. Stat. vol. 43 pp. 303-307, 1972.