Asymptotic Dissipativity of Random Processes with Impulse Perturbation in the Poisson Approximation Scheme*

Abstract

The authors analyze asymptotic dissipation of pre-limit normalized stochastic evolutionary system in ergodic Markov environment, which significantly influences the behavior of the limiting process.

This is a preview of subscription content, log in to check access.

References

  1. 1.

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

    Google Scholar 

  2. 2.

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

    Google Scholar 

  3. 3.

    V. S. Koroliuk, N. Limnios, and I. V. Samoilenko, “Levy and Poisson approximations of switched stochastic systems by a semimartingale approach,” Comptes Rendus Mathematique, Vol. 354, 723–728 (2016).

    Article  MATH  Google Scholar 

  4. 4.

    A. V. Nikitin and U. T. Khimka, “Asymptotics of normalized control with Markov switchings,” Ukr. Math. J., Vol. 68, No. 8, 1252–1262 (2017).

    MathSciNet  Article  Google Scholar 

  5. 5.

    A. V. Nikitin, “Asymptotic properties of a stochastic diffusion transfer process with an equilibrium point of a quality criterion,” Cybern. Syst. Analysis, Vol. 51, No. 4, 650–656 (2015).

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Ya. M. Chabanyuk, “Approximation by a diffusion process in averaging scheme,” Dopov. Nac. Akad. Nauk Ukr., No. 12, 35–40 (2004).

  7. 7.

    I. V. Samoilenko, Y. M. Chabanyuk, A. V. Nikitin, and U. T. Himka, “Differential equations with small stochastic additions under Poisson approximation conditions,” Cybern. Syst. Analysis, Vol. 53, No. 3, 410–416 (2017).

    Article  MATH  Google Scholar 

  8. 8.

    S. A. Semenyuk and Ya. M. Chabanyuk, “Stochastic evolutionary systems with impulse perturbation,” Visnyk Nac. Univer. “L’vivs’ka Politekhnika,” Ser. Fiz.-Mat. Nauky, Issue 660, 56–60 (2009).

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to I. V. Samoilenko.

Additional information

*The study was financially supported by the grant of the President of Ukraine (Project 0117U007015 of the State Fund for Fundamental Research).

Translated from Kibernetika i Sistemnyi Analiz, No. 2, March–April, 2018, pp. 38–44.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Samoilenko, I.V., Chabanyuk, Y.M. & Nikitin, A.V. Asymptotic Dissipativity of Random Processes with Impulse Perturbation in the Poisson Approximation Scheme*. Cybern Syst Anal 54, 205–211 (2018). https://doi.org/10.1007/s10559-018-0021-4

Download citation

Keywords

  • dissipation
  • Markov process
  • generator
  • Poisson approximation