Ukrainian Mathematical Journal

, Volume 49, Issue 7, pp 1016–1022 | Cite as

On one generalization of the averaging method

  • K. G. Valeev
  • I. A. Dzhalladova


We consider one case where it is possible to establish sufficient conditions for the convergence and analyticity of matrix series used for the construction of a system of moment equations.


Markov Process Linear Differential Equation Moment Equation Ukrainian Academy Integral Manifold 
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.


  1. 1.
    N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1974).zbMATHGoogle Scholar
  2. 2.
    N. N. Bogolyubov, Yu. A. Mitropol'skii and A. M. Samoilenko, Method of Accelerated Convergence in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1969).Google Scholar
  3. 3.
    V. M. Alekseev and K. G. Valeev, “Investigation of oscillations of a linear system with random coefficients,” Izv. Vyssh. Uchebn. Zaved., Ser. Radiophys., 14, No. 12, 1811–1815 (1971).MathSciNetGoogle Scholar
  4. 4.
    V. I. Tikhonov and M. I. Mironov, Markov Processes [in Russian], Sovetskoe Radio, Moscow (1977).zbMATHGoogle Scholar
  5. 5.
    G. N. Mil'shtein, “On the stability of a linear system under the influence of a Markov chain,” Differents. Uravn., 6, No. 11, 1982–1993 (1970).Google Scholar
  6. 6.
    K. G. Valeev and O. L. Strizhak, Method of Moment Equations [in Russian], Institute of Electrodynamics, Ukrainian Academy of Sciences, Kiev (1986).Google Scholar
  7. 7.
    K. G. Valeev and O. A. Zhautykov, Infinite Systems of Differential Equations [in Russian], Nauka, Alma-Ata (1974).Google Scholar
  8. 8.
    K. G. Valeev, Splitting of Matrix Spectrum [in Russian], Vyshcha Shkola, Kiev (1986).Google Scholar
  9. 9.
    E. F. Tsar'kov, Markov Perturbations of Parameters of Linear Differential Equations. Ergodic Theorems and Markov Processes [in Russian], Preprint No. 26, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • K. G. Valeev
  • I. A. Dzhalladova

There are no affiliations available

Personalised recommendations