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).
MSC:
| 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 |
Keywords:
Lyapunov index; asymptotic stability; second-order linear stochastic systems; white noises; explicit formulas; Stratonovich systemsReferences:
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| [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: Nauka Moscow · Zbl 0463.41020 |
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