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Solution of the Problem of Stochastic Stability of an Integral Manifold by the Second Lyapunov Method

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Ukrainian Mathematical Journal Aims and scope

By the method of Lyapunov functions, we establish sufficient conditions of stability and asymptotic stability in probability for the integral manifold of the Itô differential equations in the presence of random perturbations from the class of processes with independent increments. Theorems on stochastic stability of the analytically given integral manifold of differential equations are proved in the first approximation and under the permanent action of small (in the mean) random perturbations.

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Authors and Affiliations

  1. Al-Farabi Kazakh National University, Institute of Mathematics of the Ministry of Education and Science of Kazakhstan Republic, Alma-Ata, Kazakhstan

    G. K. Vasilina & M. I. Tleubergenov

Authors
  1. G. K. Vasilina
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  2. M. I. Tleubergenov
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 1, pp. 14–27, January, 2016.

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Vasilina, G.K., Tleubergenov, M.I. Solution of the Problem of Stochastic Stability of an Integral Manifold by the Second Lyapunov Method. Ukr Math J 68, 14–28 (2016). https://doi.org/10.1007/s11253-016-1205-6

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  • DOI: https://doi.org/10.1007/s11253-016-1205-6

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