Abstract
Sufficient mean-square stability conditions of a harmonic oscillator whose random parameter is an Ornstein-Uhlenbeck process are obtained.
References
R. Z. Khas'minskii, Stability of Systems of Differential Equations with Randomly Perturbed Parameters [in Russian], Nauka, Moscow (1969), 367 pp.
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.
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.
Yu. L. Daletskii and S. V. Fomin, Measures and Differential Equations in Infinite-Dimensional Spaces [in Russian], Nauka, Moscow (1983), 384 pp.
R. V. Bobrik, “On a property of stable systems of linear stochastic equations,” Ukr. Mat. Zh.,42, No. 2, 147–152 (1990).
Author information
Authors and Affiliations
Additional information
Translated from Ukrayins'kyy Matematychnyy Zhurnal, Vol. 44, No. 9, pp. 1276–1278, September, 1992.
Rights 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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01058379