| Title:
|
A contractive property in finite state Markov chains (English) |
| Author:
|
Kratochvíl, Petr |
| Author:
|
Lešanovský, Antonín |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
35 |
| Issue:
|
3 |
| Year:
|
1985 |
| Pages:
|
491-509 |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
15A51 |
| MSC:
|
60J10 |
| idZBL:
|
Zbl 0601.60072 |
| idMR:
|
MR803042 |
| DOI:
|
10.21136/CMJ.1985.102037 |
| . |
| Date available:
|
2008-06-09T15:06:34Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/102037 |
| . |
| Reference:
|
[1] F. L. Bauer E. Deutsch J. Stoer: Abschätzungen für die Eigenwerte positiver linearen Operatoren.Linear Algebra and Applications, 2 (1969), 275-331. MR 0245587 |
| Reference:
|
[2] G Birkhoff: Lattice Theory.3rd ed.. Amer. Math. Soc. Colloq. Publ. Vol. XXV, Providence, R. I.(1967). Zbl 0153.02501, MR 0227053 |
| Reference:
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[3] K. L. Chung: Markov chains with stationary transition probabilities.Springer-Verlag, Berlin-Göttingen-Heidelberg (1960). Zbl 0092.34304, MR 0116388 |
| Reference:
|
[4] R. L. Dobrushin: Central limit theorem for non-stationary Markov chains I, II.Theory Prob. Apl. 1 (1956), 63-80, 329-383 (EngHsh translation). Zbl 0093.15001, MR 0086436 |
| Reference:
|
[5] J. Hajnal: Weak ergodicity in non-homogeneous Markov chains.Proc. Camb. Phil. Soc. 54(1958), 233-246. Zbl 0082.34501, MR 0096306, 10.1017/S0305004100033399 |
| Reference:
|
[6] S. Karlin: A first course in stochastic processes.Academic Press, New York and London (1968). Zbl 0177.21102, MR 0208657 |
| Reference:
|
[7] J. G. Kemeny J. L. Snell: Finite Markov chains.D. van Nostrand Соrр., New York (1960). MR 0115196 |
| Reference:
|
[8] D. G. Kendall: Unitary dilatations of Markov transition operators, and the corresponding integral representations for transition-probability matrices.In: Probability and Statistics, The Harald Cramer Volume, U. Grenander (ed.), Stockholm Almqvist and Wiksell (New York: John Wiley and Sons) (1959). MR 0116389 |
| Reference:
|
[9] D. G. Kendall: Geometric ergodicity and the theory of queues.In: Mathematical methods in the social sciences, K. J. Arrow, S. Karlin, P. Suppes (ed.), Stanford, California (1960). MR 0124088 |
| Reference:
|
[10] P. Kratochvíl: On convergence of homogeneous Markov chains.Apl. mat. 28 (1983), 2, 116-119. MR 0695185 |
| Reference:
|
[11] A. Paz: Introduction to Probabilistic Automata.Academic Press, New York (1971). Zbl 0234.94055, MR 0289222 |
| Reference:
|
[12] T. A. Сарымсаков: Основы теории процессов Наркова.Государственное издателство технико-теоретической литературы, Москва (1954). Zbl 0995.90535 |
| Reference:
|
[13] Т. А. Sarymsakov: On the theory of inhomogeneous Markov chains.(in Russian). Dokl, Akad. Nauk Uzbek. S.S.R. 8 (1956), 3-7. |
| Reference:
|
[14] E. Seneta: On the historical development of the theory of finite inhomogeneous Markov chains.Proc. Camb. Phil. Soc. 74 (1973), 507-513. Zbl 0271.60074, MR 0331522, 10.1017/S0305004100077276 |
| Reference:
|
[15] E. Seneta: Coefficients of ergodicity. Structure and applications.Adv. Appl. Prob. 11 (1979), 576-590. Zbl 0406.60060, MR 0533060, 10.1017/S000186780003281X |
| Reference:
|
[16] D. Vere-Jones: Geometric ergodicity in denumerable Markov chains.Quart. J. Math. Oxford (2), 13 (1962), 7-28. Zbl 0104.11805, MR 0141160, 10.1093/qmath/13.1.7 |
| . |
