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Asymptotic expansion of a semi-Markov random evolution

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Abstract

We determine the regular and singular components of the asymptotic expansion of a semi-Markov random evolution and show the regularity of boundary conditions. In addition, we propose an algorithm for finding initial conditions for t = 0 in explicit form using the boundary conditions for the singular component of the expansion.

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References

  1. V. S. Korolyuk, “Stochastic systems with averaging in the scheme of diffusion approximation,” Ukr. Mat. Zh., 57, No. 9, 1235–1252 (2005).

    Google Scholar 

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

    MATH  Google Scholar 

  3. A. B. Vasil’eva and V. F. Butuzov, Asymptotic Methods in the Theory of Singular Perturbations [in Russian], Vysshaya Shkola, Moscow (1990).

    MATH  Google Scholar 

  4. V. S. Korolyuk, “Boundary layer in asymptotic analysis for random walks,” Theory Stochast. Process., 1–2, 25–36 (1998).

    MathSciNet  Google Scholar 

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

    Google Scholar 

  6. A. Tadzhiev, “Asymptotic expansion for the absorption-time distribution of a semi-Markov process,” Ukr. Mat. Zh., 30, No. 3, 422–426 (1978).

    Google Scholar 

  7. I. V. Samoilenko, “Asymptotic expansion for the functional of Markovian evolution in R d in the circuit of diffusion approximation,” J. Appl. Math. Stochast. Analysis, No. 3, 247–258 (2005).

  8. V. S. Korolyuk and A. F. Turbin, Mathematical Foundation of State Lumping of Large Systems, Kluwer, Dordrecht (1990).

    Google Scholar 

  9. V. S. Korolyuk and A. F. Turbin, Semi-Markov Processes and Their Applications [in Russian], Naukova Dumka, Kiev (1976).

    MATH  Google Scholar 

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

    MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv

    I. V. Samoilenko

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  1. I. V. Samoilenko
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 9, pp. 1234–1248, September, 2006.

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Samoilenko, I.V. Asymptotic expansion of a semi-Markov random evolution. Ukr Math J 58, 1396–1414 (2006). https://doi.org/10.1007/s11253-006-0139-9

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  • DOI: https://doi.org/10.1007/s11253-006-0139-9

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