| Title:
|
Integral representations for transition probabilities of Markov chains with a general state space (English) |
| Author:
|
Šidák, Zbyněk |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
12 |
| Issue:
|
4 |
| Year:
|
1962 |
| Pages:
|
492-522 |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
60.65 |
| idZBL:
|
Zbl 0121.13105 |
| idMR:
|
MR0148115 |
| DOI:
|
10.21136/CMJ.1962.100535 |
| . |
| Date available:
|
2008-06-09T13:15:57Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/100535 |
| . |
| Reference:
|
[1] J. L. Doob: One-parameter families of transformations.Duke Math. J. 4 (1938), 752 - 774. Zbl 0020.10902, MR 1546095, 10.1215/S0012-7094-38-00466-1 |
| Reference:
|
[2] J. L. Doob: Stochastic processes.New York 1953. Zbl 0053.26802, MR 0058896 |
| Reference:
|
[3] N. Dunford J. T. Schwartz: Linear operators I.Interscience Publishers, New York 1958. MR 0117523 |
| Reference:
|
[4] W. Feller: Non-Markovian processes with the semigroup property.Annals of Math. Stat. 30 (1959), 1252-1253. MR 0110124, 10.1214/aoms/1177706110 |
| Reference:
|
[5] P. Halmos: Measure theory.New York 1950. Zbl 0040.16802, MR 0033869 |
| Reference:
|
[6] T. E. Harris: The existence of stationary measures for certain Markov processes.Proc. Third Berkeley Symposium, 1956, vol. II, 113 - 124. Zbl 0072.35201, MR 0084889 |
| Reference:
|
[7] D. G. Kendall: Integral representations for Markov transition probabilities.Bull. Amer. Math. Soc. 64 (1958), 358-362. Zbl 0198.22801, MR 0126880, 10.1090/S0002-9904-1958-10230-X |
| Reference:
|
[8] D. G. Kendall: Unitary dilations of Markov transition operators, and the corresponding integral representations for transition-probability matrices.Probability & Statistics, The Harald Cramér Volume, New York 1959, 139-161. Zbl 0117.35801, MR 0116389 |
| Reference:
|
[9] D. G. Kendall: Unitary dilations of one-parameter semigroups of Markov transition operators, and the corresponding integral representations for Markov processes with a countable infinity of states.Proc. London Math. Soc. (3) 9 (1959), 417 - 431. Zbl 0117.35802, MR 0116390 |
| Reference:
|
[10] A. N. Kolmogorov: Zur Theorie der Markoffschen Ketten.Math. Ann. 112 (1936), 155 - 160. MR 1513044, 10.1007/BF01565412 |
| Reference:
|
[11] H. P. Kramer: Symmetrizable Markov matrices.Annals of Math. Stat. 30 (1959), 149 - 153. Zbl 0146.38601, MR 0103542, 10.1214/aoms/1177706367 |
| Reference:
|
[12] S. Leader: The theory of $L^p$-spaces for finitely additive set functions.Ann. of Math. 58 (1953), 528-543. MR 0058126, 10.2307/1969752 |
| Reference:
|
[13] E. Nelson: The adjoint Markoff process.Duke Math. J. 25 (1958), 671-690. Zbl 0084.13402, MR 0101555, 10.1215/S0012-7094-58-02561-4 |
| Reference:
|
[14] S. Orey: Recurrent Markov chains.Pacific J. Math. 9 (1959), 805 - 827. Zbl 0095.32902, MR 0125632, 10.2140/pjm.1959.9.805 |
| Reference:
|
[15] Т. А. Сарымсаков: Основы теории процессов Маркова.Москва 1954. Zbl 0995.90535 |
| Reference:
|
[16] В. Sz.-Nagy: Sur les contractions de l'espace de Hubert.Acta Sci. Math. Szeged 15 (1953 - 54), 87-92. MR 0058128 |
| Reference:
|
[17] K. Yosida S. Kakutani: Operator theoretical treatment of Markoff's process and mean ergodic theorem.Ann. of Math. 42 (1941), 188 - 228. MR 0003512, 10.2307/1968993 |
| Reference:
|
[18] A. Zygmund: Trigonometric series.Cambridge 1959. Zbl 0085.05601 |
| . |
