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Functions of Markov processes. (English) Zbl 0295.60064


MSC:

60J99 Markov processes
Full Text: DOI

References:

[1] Burke, C. J.; Rosenblatt, M., A Markovian function of a Markov chain, Ann. math. Statistics, 29, 1112-1122 (1958) · Zbl 0100.34402
[2] Dunford, N.; Schwartz, J. T., Linear operators (1958), New York: Interscience, New York · Zbl 0084.10402
[3] Dynkin, E. B., Markov processes, Vol. 1 (1965), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0132.37901
[4] Feller, W., Non-Markovian processes with the semigroup property, Ann. math. Statistics, 30, 1252-1253 (1959) · Zbl 0101.11001
[5] Hachigian, J., Collapsed Markov chains and the Chapman-Kolmogorov equation, Ann. math. Statistics, 34, 233-237 (1963) · Zbl 0144.18702
[6] Hachigian, J.; Rosenblatt, M., Functions of reversible Markov processes that are Markovian, J. Math. Mech., 11, 951-960 (1962) · Zbl 0115.13603
[7] Kac, M., Probability and related topics in physical sciences (1959), New York: Interscience, New York · Zbl 0087.33003
[8] Levy, P., Example de processus pseudo-Markovians, C. r. Acad. Sci., Paris, 228, 2004-2006 (1949) · Zbl 0041.25201
[9] Rosenblatt, D., Aggregation in matrix models of resource flows, American Statistician, 19, No. 3, 36-39 (1965)
[10] Rosenblatt, M., Functions of a Markov process that are Markovian, J. Math. Mech, 8, 585-596 (1959) · Zbl 0100.34403
[11] Rosenblatt, M.; Slepian, D., N^[h order Markov chains with every N variables independent, J. Soc. industr. appl. Math., 10, 538-549 (1962) · Zbl 0154.43103
[12] Sarmanov, O. V.; Zakharov, V. K., Aggregation of states in Markov chains, Teor. Probab. Appl., 8, 212-213 (1963) · Zbl 0143.20001
[13] Nagy, B. S., Extensions of linear transformations in Hilbert space which extend beyond this space (1960), New York: F. Unger, New York
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