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Asymptotic analysis of phase averaging of a transport process

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Ukrainian Mathematical Journal Aims and scope

We investigate asymptotic expansions of solutions of singularly perturbed transport equations in Markov and semi-Markov media.

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References

  1. V. S. Korolyuk and A. F. Turbin, Mathematical Foundations of Phase Lumping of Complex Systems [in Russian], Naukova Dumka, Kiev (1978).

    Google Scholar 

  2. V. S. Korolyuk, I. P. Penev, and A. F. Turbin, “Asymptotic expansion for distributions of the time of absorption of a Markov chain,” Kibernetika, 4, 133–135 (1973).

    Google Scholar 

  3. V. S. Korolyuk and A. Tadzhiev, “Asymptotic expansion for the distribution of the time of absorption of a semi-Markov process,” Dokl. Akad. Nauk Ukr. SSR, No. 12, 133–135 (1977).

    Google Scholar 

  4. V. S. Korolyuk and Yu. V. Borovskikh, Analytic Problems of Asymptotics of Probability Distributions [in Russian], Naukova Dumka, Kiev (1981).

    Google Scholar 

  5. V. S. Korolyuk and A. F. Turbin, Markov Renewal Processes in Problems of Reliability of Systems [in Russian], Naukova Dumka, Kiev (1982).

    MATH  Google Scholar 

  6. A. F. Turbin and B. G. Levinskii, “A method for asymptotic analysis of semi-Markov processes in the scheme of phase lumping,” in: Analytic Methods in Probability Theory [in Russian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (1981), pp. 133–147.

  7. A. F. Turbin, Limit Theorems for Perturbed Semigroups and Markov Processes in the Scheme of Asymptotic Phase Lumping [in Russian], Preprint No. 80.18, Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev (1981), pp. 133–147.

  8. S. Albeverio, V. Koroliuk, and I. Samoilenko, Asymptotic Expansion of Semi-Markov Random Evolutions, Preprint No. 277, SFB611, Bonn (2006).

  9. V. S. Korolyuk and N. Limnios, Stochastic Systems in Merging Phase Space, World Scientific, Singapore (2005).

    Book  Google Scholar 

  10. V. S. Korolyuk and A. V. Svishchuk, Semi-Markov Random Evolutions [in Russian], Naukova Dumka, Kiev (1992).

    MATH  Google Scholar 

  11. V. S. Korolyuk and V. V. Korolyuk, Stochastic Models of Systems, Kluwer, Dordrecht (1999).

    MATH  Google Scholar 

  12. A. N. Korlat, V. N. Kuznetsov, M. M. Novikov, and A. F. Turbin, Semi-Markov Models of Renewable Systems and Queuing Systems [in Russian], Shtiintsa, Kishinev (1973).

    Google Scholar 

  13. M. A. Pinsky, Lectures on Random Evolution, World Scientific, New Jersey (1991).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Zhytomyr University, Zhytomyr, Ukraine

    A. O. Pohorui

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  1. A. O. Pohorui
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 2, pp. 190–198, February, 2010.

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Pohorui, A.O. Asymptotic analysis of phase averaging of a transport process. Ukr Math J 62, 210–221 (2010). https://doi.org/10.1007/s11253-010-0345-3

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  • DOI: https://doi.org/10.1007/s11253-010-0345-3

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