Abstract
We establish asymptotic estimates for the behavior of the distribution of the time of the first hit of an infinitely remote level by a semi-Markov process on a semiaxis of integer numbers.
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References
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V. S. Korolyuk, A. F. Turbin, and A. A. Tomusyak, “Time of stay of a semi-Markov process in an expanding set of states,” in:Analytic Methods in Probability Theory [in Russian], Naukova Dumka, Kiev (1979), pp. 62–69.
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A. A. Pogorui, “Asymptotic expansion of the distribution of the time of the first hit of an infinitely remote level by a semi-Markov process,” in:Random Evolutions: Theoretical and Applied Problems [in Russian], Naukova Dumka, Kiev (1992), pp. 69–76.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 11, pp. 1586–1590, November, 1994.
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Pogorui, A.A. Asymptotic inequalities for the distribution of the time of stay of a semi-Markov process in an expanding set of states. Ukr Math J 46, 1757–1762 (1994). https://doi.org/10.1007/BF01058896
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DOI: https://doi.org/10.1007/BF01058896