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References
Blackwell, D.: The existence of anormal chains. Bull. Amer. math. Soc. 51, 465–468 (1945).
Chacon, R. V.: Identification of the limit of operator averages. J. Math. and Mech. 11, 961–968 (1962).
Chung, K. L.: The general theory of Markov processes according to Doeblin. Z. Wahrscheinlichkeitstheorie verw. Geb. 2, 230–254 (1964).
—: Markov chains with stationary transition probabilities. Berlin-Göttingen-Heidelberg: Springer 1960.
Derman, C.: Some contributions to the theory of denumerable Markov chains. Trans. Amer. math. Soc. 79, 541–555 (1955).
Doeblin, W.: Sur les propriétés asymptotiques de mouvement régis par certains types de chaÎns simples. Bull. math. Soc. Roumaine Sci. 39, No. 1, 57–115; No. 2, 3–61 (1937).
—: Eléments d'une théorie générale des chaÎnes simple constantes de Markoff. Ann. sci. école norm. sup., III. Sér., 57, 61–111 (1940).
Doob, J. L.: Stochastic processes. New York: Wiley and Sons 1953.
—: Asymptotic properties of Markoff transition probabilities. Trans. Amer. math. Soc. 63, 393–438 (1948).
Foguel, S. R.: Limit theorems for Markov processes. Trans. Amer. math. Soc. 121, 200–209 (1966).
Harris, T. E.: The existence of stationary measures for certain Markov processes. Proc. Third Berkeley Sympos. math. Statist. Probability II, 113–124 (1956).
Isaac, R.: Non-singular recurrent Markov processes have stationary measures. Ann. math. Statistics 35, 869–871 (1964).
Jain, N. C.: Some limit theorems for a general Markov process. Z. Wahrscheinlichkeitstheorie verw. Geb. 6, 206–223 (1966).
Jamison, B., and S. Orey: Tail σ-field of Markov processes recurrent in the sense of Harris. To appear.
Moy, S. T. C.: λ-continuous Markov chains. Trans. Amer. math. Soc. 117, 68–91 (1965).
—: λ-continuous Markov chains II. Trans. Amer. math. Soc. 120, 83–107 (1966).
Nelson, E.: The adjoint Markoff process. Duke math. J. 25, 671–690 (1958).
Orey, S.: Recurrent Markov chains. Pacific J. Math. 9, 805–827 (1959).
šidák, Z.: Classification of Markov chains with a general state space. Bull. Amer. math. Soc. 72, 149–152 (1966).
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Both authors were partially supported by the Air Force Office of Scientific Research.
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Jain, N., Jamison, B. Contributions to Doeblin's theory of Markov processes. Z. Wahrscheinlichkeitstheorie verw Gebiete 8, 19–40 (1967). https://doi.org/10.1007/BF00533942
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DOI: https://doi.org/10.1007/BF00533942