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References
D. G. Austin, On the existence of the derivative of Markoff transition probability functions.Proc. Nat. Acad. Sci. U.S.A., 41 (1955), 224–226.
K. L. Chung, Some new developments in Markov chains,Trans. Am. Math. Soc., 81 (1956), 195–210.
R. L. Dobrušin, On conditions of regularity of stationary Markov processes with a denumerable number of possible states.Uspehi Matem. Nauk (N. S.), 7 (1952), 185–191.
J. L. Doob, Markoff chains—denumerable case.Trans. Am. Math. Soc., 58 (1945), 455–473.
J. L. Doob,Stochastic Processes. New York & London. 1953.
W. Feller, On the integro-differential equations of purely discontinuous Markoff process.Trans. Am. Math. Soc., 48 (1940), 488–515;ibid., 58 (1945), 474.
W. Feller,An Introduction to Probability Theory and Its Applications, I. New York & London, 1950.
—, Boundaries induced by non-negative matrices.Trans. Am. Math. Soc., 83 (1956), 19–54.
W. Feller, On boundary conditions for the Kolmogorov differential equations (to appear).
E. Hille,Functional Analysis and Semi-Groups. New York, 1948.
E. Hille, On the generation of semi-groups and the theory of conjugate functions.Kungl. Fysiografiska Sällskapets i Lund Förhandlingar, 21 (1952), No. 14.
—, Perturbation methods in the study of Kolmogorov's equations.Proceedings of the International Congress of Mathematicians (1954), Vol. III, 365–376.
A. Jensen,A Distribution Model. Copenhagen, 1954.
S. Karlin &J. McGregor, Representation of a class of stochastic processes.Proc. Nat. Acad. Sci. 41 (1955), 387–391.
T. Kato, On the semigroups generated by Kolmogoroff's differential equations.J. Math. Soc. Japan, 6 (1954), 1–15.
D. G. Kendall, Some analytical properties of continuous stationary Markov transition functions.Trans. Am. Math. Soc., 78 (1955), 529–540.
—, Some further pathological examples in the the theory of denumerable Markov processes.Quart. J. of Math. Oxford (Ser. 2), 7 (1956), 39–56.
D. G. Kendall &G. E. H. Reuter, Some pathological Markov processes with a denumerable infinity of states and the associated semigroups of operators inl.Proceedings of the International Congress of Mathematicians (1954), Vol. III, 377–415.
A. N. Kolmogorov, On the differentiability of the transition probabilities in stationary Markov processes with a denumerable number of states.Moskov. Gos. Univ. Učenye Zapiski Matematika, 148 (1951), 53–59.
W. Ledermann &G. E. H. Reuter, Spectral theory for the differential equations of simple birth ard death processes.Phil. Trans. Roy. Soc. London (Ser. A), 246 (1954), 321–369.
P. Lévy, Systèmes markoviens et stationnaires; cas dénombrable,Ann. Sci. École-Norm. Sup. (3), 68 (1951), 327–381.
G. E. H. Reuter, A note on contraction semigroups.Math. Scand., 3 (1956), 275–280.
G. E. H. Reuter &W. Ledermann, On the differential equations for the transition probabilities of Markov processes with enumerably many states.Proc. Camb. Phil. Soc., 49 (1953), 247–262.
K. Yosida, On the differentiability and the representation of one-parameter semi-groups of linear operators.J. Math. Soc. Japan, 1 (1948), 15–21.
—, An operator-theoretical treatment of temporally homogenous MMarkoff process.Ibid.,, 1 (1949), 244–253.
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Reuter, G.E.H. Denumerable Markov processes and the associated contraction semigroups onl . Acta Math. 97, 1–46 (1957). https://doi.org/10.1007/BF02392391
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DOI: https://doi.org/10.1007/BF02392391