Cybernetics and Systems Analysis

, Volume 54, Issue 2, pp 205–211 | Cite as

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

  • I. V. SamoilenkoEmail author
  • Y. M. Chabanyuk
  • A. V. Nikitin


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.


dissipation Markov process generator Poisson approximation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. S. Korolyuk and V. V. Korolyuk, Stochastic Models of Systems, Kluwer, Dordrecht (1999).CrossRefzbMATHGoogle Scholar
  2. 2.
    V. S. Koroliuk and N. Limnios, Stochastic Systems in Merging Phase Space, World Scientific, Singapore (2005).CrossRefzbMATHGoogle 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).CrossRefzbMATHGoogle 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).MathSciNetCrossRefGoogle 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).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ya. M. Chabanyuk, “Approximation by a diffusion process in averaging scheme,” Dopov. Nac. Akad. Nauk Ukr., No. 12, 35–40 (2004).Google Scholar
  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).CrossRefzbMATHGoogle 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).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • I. V. Samoilenko
    • 1
    Email author
  • Y. M. Chabanyuk
    • 2
  • A. V. Nikitin
    • 1
  1. 1.Taras Shevchenko National University of KyivKyivUkraine
  2. 2.Lublin University of Technology (Politechnika Lubelska)LublinPoland

Personalised recommendations