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Asymptotic expansions of the Lyapunov index for linear stochastic systems with small noise. (English. Russian original) Zbl 0522.34053
J. Appl. Math. Mech. 46, 277-283 (1983); translation from Prikl. Mat. Mekh. 46, 378-395 (1982).

34F05 Ordinary differential equations and systems with randomness
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
34D05 Asymptotic properties of solutions to ordinary differential equations
93E15 Stochastic stability in control theory
Full Text: DOI
[1] Khas’minskii, R.Z., Stability of systems of differential equations under random perturbations of their parameters, (1969), Nauka Moscow · Zbl 0214.15903
[2] Nevel’son, M.B., Behavior of a linear system under small, random excitation of its parameters, Pmm, Vol. 31, No. 3, (1967) · Zbl 0189.17503
[3] Nevel’son, M.B., On the behavior of the invariant measure of a diffusion process with a small diffusion on a circle, Teor. veroyatn. i ee primen., Vol.9, No. 1, (1964) · Zbl 0134.34501
[4] Bernstein, S.N., Sur l’équation différentielle de Fokker-Planck, C.R. acad. sci. Paris, Vol. 196, No.15, (1933) · JFM 59.0509.01
[5] Kolmogoroff, A.N., Zur amkehbarkeit der statistischen naturgesetze, Math. ann., B.113, (1937) · Zbl 0015.26004
[6] Fedoriuk, M.V., The saddle-point method, (1977), Nauka Moscow
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