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Chung, K. L.: Markov Chains with stationary transition probabilities. Berlin-Göttingen-Heidelberg: Springer 1960.
Cohn, P. M.: Lie Groups. Cambridge: Cambridge University Press 1965.
Davidson, R.: Arithmetic and Other Properties of Certain Delphic Semigroups 1. Z. Wahrscheinlichkeitstheorie verw. Gebiete 10, 120–145 (1968).
Dobrušin, R. L.: Generalization of Kolmogorov's equations for Markov processes with a finite number of possible states. Mat. Sb. N.S. 33, (75), 567–596 (1953).
Doeblin, W.: Sur certains mouvements aléatoires discontinus. Skand. Aktuarietidskr. 22, 211–222 (1939).
Doob, J.L.: Stochastic Processes. New York: Wiley 1953.
Elfving, G.: Zur Theorie der Markoffschen Ketten. Acta Soc. Sci. Fennicae, n. Ser. A2, No. 8, 1–17 (1937).
Elfving, G.: über die Interpolation von Markoffschen Ketten. Soc. Sci. Fenn. Comment. Phys.-Math. 10, No. 3, 1–8 (1939).
Feller, W.: On the integro-differential equations of purely discontinuous processes. Trans. Amer. Math. Soc. 48, 488–515 (1940).
Fréchet, M.: Recherches théoriques moderne sur le calcul des probabilitiés, Ile livre. Paris: Gauthier-Villars 1938.
Gnedenko, B.W., Kolmogorov, A.N.: Grenzverteilungen von Summen unabhÄngiger Zufallsgrö\en. Berlin: Akademie-Verlag 1959.
Goodman, G.: An Intrinsic Time for Non-Stationary Finite Markov Chains. Z. Wahrscheinlichkeitstheorie verw. Gebiete 16, 165–180 (1970).
Johansen, S.: The Bang-Bang Problem for Stochastic Matrices. Z. Wahrscheinlichkeitstheorie verw. Gebiete 26, 191–195 (1973).
Grenander, U.: Probabilities on Algebraic Structures. New York: Wiley 1963.
Johansen, S.: A relation between the imbedding problem for finite Markov Chains and infinitely divisible distributions on certain semi groups. J. London Math. Soc. (In press).
Kendall, D.G.: Delphic semigroups, infinitely divisible regenerative phenomena, and the arithmetic of p-functions. Z. Wahrscheinlichkeitstheorie verw. Gebiete 9, 163–195 (1968).
Kingman, J. F. C.: The imbedding problem for finite Markov Chains. Z. Wahrscheinlichkeitstheorie verw. Gebiete 1, 14–24 (1962).
Loewner, C.: A Theorem on the partial order derived from a certain transformation semigroup. Math. Z. 72, 53–60 (1959).
Loewner, K.: Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I. Math. Ann. 89, 103–121 (1923).
MacNernay, J.S.: A nonlinear integral operation. Illinois J. Math. 8, 621–638 (1964).
Martin-Löf, P.: Probability Theory on Discrete Semigroups. Z. Wahrscheinlichkeitstheorie verw. Gebiete 4, 78–101 (1965).
Schlesinger, L.: Neue Grundlagen für einen Infinitesimalkalkül der Matrisen. Math. Z. 33, 33–61 (1931).
Maksimov, B. M.: On divisible distributions on finite groups. Theor. Probability Appl. 16, 306–318 (In Russian) (1971).
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Johansen, S. A central limit theorem for finite semigroups and its application to the imbedding problem for finite state Markov chains. Z. Wahrscheinlichkeitstheorie verw Gebiete 26, 171–190 (1973). https://doi.org/10.1007/BF00532720
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DOI: https://doi.org/10.1007/BF00532720