Skip to main content
Log in

On the mean-square stability for a harmonic oscillator with random parameter

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

Sufficient mean-square stability conditions of a harmonic oscillator whose random parameter is an Ornstein-Uhlenbeck process are obtained.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. R. Z. Khas'minskii, Stability of Systems of Differential Equations with Randomly Perturbed Parameters [in Russian], Nauka, Moscow (1969), 367 pp.

    Google Scholar 

  2. S. V. Anulova, A. Yu. Veretennikov, N. V. Krylov, et al., “Stochastic calculus,” in: Itogi Nauki i Tekhniki (Modern Problems in Mathematics. Fundamental Trends), Vol. 49, VINITI (1989), 5–260.

    Google Scholar 

  3. I. I. Gikhman, “On the stability of the solutions of stochastic differential equations,” in: Limit Theorems and Statistical Inference, Institute of Mathematics of the Academy of Sciences of the Uzbek SSR, Tashkent (1966), 14–45.

    Google Scholar 

  4. Yu. L. Daletskii and S. V. Fomin, Measures and Differential Equations in Infinite-Dimensional Spaces [in Russian], Nauka, Moscow (1983), 384 pp.

    Google Scholar 

  5. R. V. Bobrik, “On a property of stable systems of linear stochastic equations,” Ukr. Mat. Zh.,42, No. 2, 147–152 (1990).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrayins'kyy Matematychnyy Zhurnal, Vol. 44, No. 9, pp. 1276–1278, September, 1992.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bobryk, R.V. On the mean-square stability for a harmonic oscillator with random parameter. Ukr Math J 44, 1167–1169 (1992). https://doi.org/10.1007/BF01058379

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01058379

Keywords

Navigation