Isomorphism and approximation of general state Markov processes

Isaac, Richard

doi:10.1090/S0002-9947-1969-0242256-1

Isomorphism and approximation of general state Markov processes
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by Richard Isaac

Trans. Amer. Math. Soc. 140 (1969), 367-380

DOI: https://doi.org/10.1090/S0002-9947-1969-0242256-1

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References

David Blackwell, Idempotent Markoff chains, Ann. of Math. (2) 43 (1942), 560–567. MR 6632, DOI 10.2307/1968811
R. V. Chacon, Identification of the limit of operator averages, J. Math. Mech. 11 (1962), 961–968. MR 0145352
J. L. Doob, Stochastic processes, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1953. MR 0058896

Linear operators

William Feller, An introduction to probability theory and its applications. Vol. I, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1957. 2nd ed. MR 0088081
Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869, DOI 10.1007/978-1-4684-9440-2
Paul R. Halmos and John von Neumann, Operator methods in classical mechanics. II, Ann. of Math. (2) 43 (1942), 332–350. MR 6617, DOI 10.2307/1968872
T. E. Harris, On chains of infinite order, Pacific J. Math. 5 (1955), 707–724. MR 75482, DOI 10.2140/pjm.1955.5.707
T. E. Harris and Herbert Robbins, Ergodic theory of Markov chains admitting an infinite invariant measure, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 860–864. MR 56873, DOI 10.1073/pnas.39.8.860
Felix Hausdorff, Set theory, Chelsea Publishing Co., New York, 1957. Translated by John R. Aumann, et al. MR 0086020
Richard Isaac, On regular functions for certain Markov processes, Proc. Amer. Math. Soc. 17 (1966), 1308–1313. MR 205330, DOI 10.1090/S0002-9939-1966-0205330-4
T. E. Harris, The existence of stationary measures for certain Markov processes, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol. II, University of California Press, Berkeley-Los Angeles, Calif., 1956, pp. 113–124. MR 0084889
N. C. Jain, Some limit theorems for a general Markov process, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 6 (1966), 206–223. MR 216580, DOI 10.1007/BF00531804
John L. Kelley, General topology, D. Van Nostrand Co., Inc., Toronto-New York-London, 1955. MR 0070144
John Lamperti, Probability. A survey of the mathematical theory, W. A. Benjamin, Inc., New York-Amsterdam, 1966. MR 0206996

Convergence of random processes and limit theorems in probability theory

1

Kai Lai Chung, Markov chains with stationary transition probabilities, Die Grundlehren der mathematischen Wissenschaften, Band 104, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960. MR 0116388, DOI 10.1007/978-3-642-49686-8