Literature cited
E. I. Kaplan, A. I. Motsa, and D. S. Sil'vestrov, “Limit theorems for additive functional defined on asymptotically recursive Markov chains. I,”Teor. Veroyatn. i Mat. Stat., No. 27, 34–51 (1982).
E. I. Kaplan, A. I. Motsa, and D. S. Sil'vestrov, “Limit theorems for additive functional defined on asymptotically recursive Markov chains. II,”Teor. Veroyatn. i Mat. Stat., No. 28, 31–40 (1983).
V. S. Korolyuk and A. F. Turbin,Mathematical Foundations of Phase Enlargement of Complex Systems [in Russian], Naukova Dumka, Kiev (1978).
V. V. Anisimov and A. V. Voina, “Limit theorems for summation schemes on stochastic processes with an arbitrary state space,”Teor. Veroyatn. i Mat. Stat, No. 19, 9–17 (1978).
D. S. Sil'vestrov, “Theorems of large deviation type for the attainment times of sequences with intermixing,”Teor. Veroyatn. i Mat. Stat, No. 24, 129–135 (1981).
W. Feller,Introduction to Probability Theory and its Applications, 2 Vols., Wiley, New York (1958–1966).
Additional information
Translated fromProblemy Ustoichivosti Stokhasticheskikh Modelei. Trudy Seminara, 1988, pp. 129–137.
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Sil'vestrov, D.S., Velikii, Y.A. Necessary and sufficient conditions for convergence of attainment times. J Math Sci 57, 3317–3324 (1991). https://doi.org/10.1007/BF01099033
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DOI: https://doi.org/10.1007/BF01099033