Literature Cited
J. Kemeny and J. Snell, Finite Markov Chains, Van Nostrand Reinhold, Princeton (1960).
V. S. Korolyuk, L. I., Polishchuk, and A. A. Tomusyak, “On a limit theorem for semi-Markov processes,” Kibernetika, No. 4 (1968).
A. A. Pervozvanskii and I. N. Smirnov, “Estimation of a stationary state of a complex system with slowly changing dependences,” Kibernetika, No. 4 (1974).
F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1967).
V. B. Lidskii, “Theory of perturbations of nonself-adjoint operators.,” Zh. Vychisl. Mat. i Mat. Fiz.,6, No. 1 (1966).
Yu. L. Daletskii, “Differentiation of functions of nonhermitian matrices which depend on a parameter,” Izv. Vyssh. Uchebn. Zaved., Matematika, No. 2 (1962).
G. N. Tsertsvadze, “Asymptotic consolidation of the states of Markov chains and automata with random input effects,” Author's Abstract of Dissertation, Tbilisi State University (1971).
V. V. Anisimov, “Asymptotic consolidation of states of stochastic processes,” Kibernetika, No. 3 (1973).
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Translated from Kibernetika, No. 3, pp. 91–98, May–June, 1975.
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Gaitsgori, V.G., Pervozvanskii, A.A. Aggregation of states in a Markov chain with weak interaction. Cybern Syst Anal 11, 441–450 (1975). https://doi.org/10.1007/BF01069471
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DOI: https://doi.org/10.1007/BF01069471