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Asymptotic normality of a discrete procedure of stochastic approximation in a semi-Markov medium

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Abstract

We obtain sufficient conditions for the asymptotic normality of a jump procedure of stochastic approximation in a semi-Markov medium using a compensating operator of an extended Markov renewal process. The asymptotic representation of the compensating operator guarantees the construction of the generator of a limit diffusion process of the Ornstein-Uhlenbeck type.

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References

  1. Ya. M. Chabanyuk, “Asymptotic normality for a continuous procedure of stochastic approximation in a Markov medium,” Dopov. Nats. Akad. Nauk Ukr., Ser. A, No. 5, 37–45 (2004).

  2. V. S. Korolyuk, “Stability of stochastic systems in the diffusion-approximation scheme,” Ukr. Mat. Zh., 50, No. 1, 36–47 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  3. M. B. Nevel’son and R. Z. Khas’minskii, Stochastic Approximation and Recursive Estimation [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  4. L. Ljung, G. Pflug, and H. Walk, Stochastic Approximation and Optimization of Random Systems, Birkhäuser, Basel (1992).

    MATH  Google Scholar 

  5. V. Korolyuk and A. Swishchuk, Evolution of Systems in Random Media, CRC Press, Boca Raton-New York (1995).

    Google Scholar 

  6. Ya. M. Chabanyuk, “Continuous procedure of stochastic approximation in a semi-Markov medium,” Ukr. Mat. Zh., 56, No. 5, 713–720 (2004).

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

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

  9. A. A. Borovkov, Probability Theory [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  10. W. Feller, An Introduction to Probability Theory and Its Applications, Vols. 1, 2, Wiley, New York (1970, 1971).

    Google Scholar 

  11. A. D. Wentzell, Limit Theorems on Large Deviations for Markov Random Processes [in Russian], Nauka, Moscow (1986).

    Google Scholar 

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

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Authors and Affiliations

  1. “L’vivs’ka Politekhnika” National University, Lviv

    Ya. M. Chabanyuk

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  1. Ya. M. Chabanyuk
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 10, pp. 1425–1433, October, 2006.

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Chabanyuk, Y.M. Asymptotic normality of a discrete procedure of stochastic approximation in a semi-Markov medium. Ukr Math J 58, 1616–1625 (2006). https://doi.org/10.1007/s11253-006-0157-7

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  • DOI: https://doi.org/10.1007/s11253-006-0157-7

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