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Three examples of markov functionals

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Abstract

Three examples are considered of the application of general limit theorems for Markov functionals: to the problem of the moment of exit of a Markov process from a subset of states; to the analysis of systems of mass service with relatively rapid service; to the asymptotics of the mean number of particles in a branching process in a Markov random medium.

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Literature cited

  1. V. M. Shurenkov, Ergodic Markov Processes [in Russian], Nauka, Moscow (1989).

    Google Scholar 

  2. A. V. Skorokhod, “The construction of Markov processes with the help of multiplicative functionals,” in: Winter School in Probability Theory and Mathematical Statistics, Mathematics Institute of the Academy of Sciences of the Ukrainian SSR, Kiev (1964), pp. Kiev (1964), pp. 191–216.

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  3. D. V. Korolyuk and D. S. Sil'vestrov, “The moments of attainment of asymptotically receding regions for ergodic Markov chains,” in: Winter School in Probability Theory and Mathematical Statistics, Mathematics Institute of the Academy of Sciences of the Ukrainian SSR, Kiev,28, No. 2, 410–420 (1983).

    Google Scholar 

  4. V. V. Anisimov, Stochastic Processes with a Discrete Component. Limit Theorems [in Russian], Vishcha Shkola, Kiev (1988).

    Google Scholar 

  5. I. N. Kovalenko, N. Yu. Kuznetsov, and V. M. Shurenkov, Stochastic Processes (Handbook) [in Russian], Naukova Dumka, Kiev (1983).

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  6. B. A. Sevast'yanov, Branching Processes [in Russian], Nauka, Moscow (1971).

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 3, pp. 299–304, March, 1992.

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Alimov, D. Three examples of markov functionals. Ukr Math J 44, 259–264 (1992). https://doi.org/10.1007/BF01063125

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  • DOI: https://doi.org/10.1007/BF01063125

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