Ukrainian Mathematical Journal

, Volume 42, Issue 2, pp 129–134 | Cite as

A property of stable systems of linear stochastic equations

  • R. V. Bobrik


The relationship between exponential mean square stability of systems of linear ordinary differential equations with Gaussian coefficients and the same stability of the corresponding linear stochastic Ito differential equations is obtained.


Differential Equation Ordinary Differential Equation Stable System Stochastic Equation Linear Ordinary Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    I. I. Gikhman, “On the stability of solutions of stochastic differential equations,” in: Limit Theorems and Statistical Inference, Institute of Mathematics, Acad. Sci. UzbSSR (1966), pp. 14–45.Google Scholar
  2. 2.
    R. Z. Khas'minskii, The Stability of Systems of Differential Equations under Random Perturbation of Its Parameters [in Russian], Nauka, Moscow (1967).Google Scholar
  3. 3.
    T. Sasagawa, “Sufficient condition for the exponential p-stability and p-stabilizality,” Int. J. Syst. Sci.,13, No. 4, 399–408 (1982).Google Scholar
  4. 4.
    P. V. Pakshin, “Stability of linear and special nonlinear stochastic systems with parametric noise,” in: Dynamics of Nonhomogeneous Systems, Seminar Materials, VNII Sistem. Issled. (All-Union Scientific Research Institute of System Investigations) (1987), pp. 26–40.Google Scholar
  5. 5.
    V. I. Averbukh and O. G. Smolyanov, “Differentiation theory in linear topological spaces,” Usp. Mat. Nauk,22, No. 6, 201–260 (1967).Google Scholar
  6. 6.
    Yu. L. Daletskii and S. V. Fomin, Measures and Differential Equations in Infinite Spaces [in Russian], Nauka, Moscow (1983).Google Scholar
  7. 7.
    V. I. Klyatskin and V. I. Tatarskii, “An approximation of a diffusion random process in some nonstationary statistical problem of physics,” Usp. Fiz. Nauk,110, No. 4, 499–536 (1973).Google Scholar
  8. 8.
    H. S. Wall, Analytic Theory of Continued Fractions, van Nostrand, New York (1948).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • R. V. Bobrik
    • 1
  1. 1.Institute of Applied Problems of Mechanics and MathematicsAcademy of Sciences of the Ukrainian SSRLvov

Personalised recommendations