Literature cited
R. L. Dobrushin, “Central limit theorem for nonhomogeneous Markov chains. I; II,” Teor. Veroyatn. Primen.,1, No. 1, 72–89 (1956); No. 4, 365–425 (1956).
M. Loeve, Probability Theory, Van Nostrand, Princeton (1963).
P. Billingsley, Convergence of Probability Measures, Wiley, New York (1968).
V. V. Anisimov and M. F. Taurov, “Estimates for the rapprochement of the transition characteristics of Markov chains,” in: Abstracts of Reports. Fourth Internat. Conf. on Probability Theory and Mathematical Statistics, Vol. 1 (1985), pp. 28–29.
V. V. Anisimov, Limit Theorems for Random Processes and Their Application to Discrete Summation Schemes [in Russian], Vishcha Shkola, Kiev (1976).
V. V. Anisimov, Asymptotic Methods in the Analysis of Stochastic Systems [in Russian], Metsniereba, Tbilisi (1984).
V. V. Anisimov, “Limit theorems for nonhomogeneous weakly dependent summation schemes,” Teor. Veroyatn. Mat. Statist., No. 27, 10–22 (1982).
V. S. Korolyuk, “On the asymptotic behavior of the occupation time of a semi-Markov process in a subset of states,” Ukr. Mat. Zh.,21, No. 6, 842–845 (1969).
V. S. Korolyuk and A. F. Turbin, Semi-Markov Processes and Their Applications [in Russian], Naukova Dumka, Kiev (1976).
A. M. Zubkov, “Inequalities for restricted transition probabilities and their applications,” Mat. Sb.,109 (151), No. 4, 491–532 (1979).
A. D. Solov'ev, “Analytic Methods for the computation and the estimation of reliability,” in: Problems in the Mathematical Theory of Reliability [in Russian], Radio i Svyaz', Moscow (1983), pp. 9–112.
I. N. Kovalenko, The Analysis of Rare Events at the Estimation of System Efficiency [in Russian], Sov. Radio, Moscow (1980).
D. J. Aldous, “Markov chains with almost exponential hitting times,” Stochastic Process. Appl.,13, No. 3, 305–310 (1982).
N. V. Kartashov, “Estimates of the geometrical asymptotic behavior of first exit times,” Teor. Veroyatn. Primen.,30, No. 1, 202–203 (1985).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 40, No. 6, pp. 699–704, November–December, 1988.
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Anisimov, V.V. Estimates for the deviations of the transition characteristics of nonhomogeneous markov processes. Ukr Math J 40, 588–592 (1988). https://doi.org/10.1007/BF01057174
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DOI: https://doi.org/10.1007/BF01057174