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The tail \(\sigma\)-fields of recurrent Markov processes. (English) Zbl 0375.60075

MSC:
60J05 Discrete-time Markov processes on general state spaces
60B99 Probability theory on algebraic and topological structures
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References:
[1] Blackwell D., Freedman D.: The tail \(\sigma\)-field of a Markov chain and a theorem of Orey. Ann. Math. Stat. 35, (1964), 1291-1295. · Zbl 0127.35204
[2] Doeblin W.: Elements d’une theorie generale des chaines simples constants de Markoff. Ann. Sci. Ecole Norm. Sup., III, Ser. 57, (1940), 61-111. · Zbl 0024.26503
[3] Halmos P. R.: Measure Theory. Van Nostrand) · Zbl 0040.16802
[4] Harris T. E.: The existence of stationary measures for certain Markov processes. Third Berkeley Symposium on Math. Stat. and Prob., vol. 2(1956), 113-124. · Zbl 0072.35201
[5] Harris T. W., Robbins H.: Ergodic theory of Markov chains admitting an infinite invariant measure. Proc. Nat. Acad. Sci., 39, (1953), 860-864. · Zbl 0051.10503
[6] Isaac R.: Limit theorems for Markov transition functions. Ann. Math. Stat. 43, (1972), 621-626. · Zbl 0278.60048
[7] Isaac R.: Theorems for conditional expectation, with applications to Markov processes. Israel Journal of Math., vol. 16, no. 4 (1973), 362-374. · Zbl 0295.28021
[8] Isaac R.: A uniqueness theorem for stationary measures of ergodic Markov processes. Ann. Math. Stat. 35, (1964), 1781 - 1786. · Zbl 0127.09702
[9] Isaac R.: On regular functions for certain Markov processes. Proc. Amer. Math. Soc., 17, (1966), 1308-1313. · Zbl 0143.40502
[10] Jain N. C: A note on invariant measures. Ann. Math. Stat., 37 (1966), 729-732. · Zbl 0192.25002
[11] Jamison B., Orey S.: Markov chains recurrent in the sense of Harris. Z. F. Wahrschein, 8, (1967), 41-48. · Zbl 0153.19802
[12] Orey S.: Recurrent Markov chains. Pacific Journal, 9 (1959), 805-827. · Zbl 0095.32902
[13] Orey S.: Limit Theorems for Markov Chain Transition Probabilities. Van Nostrand (1971). · Zbl 0295.60054
[14] Foguel S. R.: The ergodic theory of Markov Processes. Van Nostrand Reinhold (1969). · Zbl 0282.60037
[15] Rosenblatt M.: Markov Processes. Structure and asymptotic behavior. Springer-Verlag (1971). · Zbl 0236.60002
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