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Analysis of oscillations in quasilinear stochastic dynamic hereditary systems

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Abstract

Oscillations in quasilinear stochastic hereditary systems and their application to specific problems are investigated. The algorithm of transition to a standard system with the help of the averaging method with small parameter in the presence of fast time is justified.

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References

  1. V. K. Yasinsky and I. V. Malyk, “Parametric continuity of solutions to stochastic functional differential equations with Poisson perturbations,” Cybern. Syst. Analysis, 48, No. 6, 846–860 (2012).

    Article  MathSciNet  Google Scholar 

  2. E. B. Dynkin, Markov Processes, Academic Press, NY (1965).

    MATH  Google Scholar 

  3. V. I. Tikhonov and M. A. Mironov, Markov Processes [in Russian], Sov. Radio, Moscow (1977).

    Google Scholar 

  4. V. S. Korolyuk and N. Limnios, Stochastic Systems in Merging Phase Space, Springer, Berlin (2005).

    Book  Google Scholar 

  5. Yu. A. Mitropol’skii, The Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka, Kyiv (1971).

    Google Scholar 

  6. E. F. Tsarkov, Random Perturbations of Functional Differential Equations [in Russian], Zinatne, Riga (1989).

    Google Scholar 

  7. R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York (1963).

    MATH  Google Scholar 

  8. B.V. Shabat, An Introduction to the Complex Analysis [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  9. J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes, Springer, Berlin (1987).

    Book  MATH  Google Scholar 

  10. I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations and their Applications [in Russian], Naukova Dumka, Kyiv (1982).

    Google Scholar 

  11. E. F. Tsarkov and V. K. Yasinsky, Quasilinear Stochastic Functional Differential Equations [in Russian], Orientir, Riga (1992).

    Google Scholar 

  12. V. K. Yasinsky and E.V. Yasinsky, Stability and Stabilization Problems for Dynamic Systems with Finite Atereffect [in Ukrainian], TVMS, Kyiv (2005).

    Google Scholar 

  13. P. Billingsley, Convergence of Probability Measures, Wiley, New York (1968).

    MATH  Google Scholar 

  14. A. Jakubovski, “A non-Skorohod topology on the Skorohod space,” Electronic J. of Probability, 42, No. 18, 1–21 (1997).

    Google Scholar 

  15. M. I. Bukatar’ and E. F. Tsarkov, “Self-oscillations in a lamp generator with a feedback with delay,” Izvestiya Vuzov, No. 8, 1117–1125 (1970).

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Authors and Affiliations

  1. Yu. Fed’kovych National University, Chernivtsi, Ukraine

    V. K. Yasinsky & I. V. Malyk

Authors
  1. V. K. Yasinsky
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  2. I. V. Malyk
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Correspondence to V. K. Yasinsky.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 3, May–June, 2013, pp. 82–95.

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Yasinsky, V.K., Malyk, I.V. Analysis of oscillations in quasilinear stochastic dynamic hereditary systems. Cybern Syst Anal 49, 397–408 (2013). https://doi.org/10.1007/s10559-013-9523-2

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  • DOI: https://doi.org/10.1007/s10559-013-9523-2

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