Asymptotic expansions of the Lyapunov index for linear stochastic systems with small noise

DOI10.1016/0021-8928(82)90099-5zbMath0522.34053OpenAlexW2043688767MaRDI QIDQ1055958

E. I. Auslender, G. N. Mil'stejn

Publication date: 1982

Published in: Journal of Applied Mathematics and Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8928(82)90099-5

zbMATH Keywords

asymptotic stabilityexplicit formulasLyapunov indexwhite noisessecond-order linear stochastic systemsStratonovich systems

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Stochastic stability in control theory (93E15) Ordinary differential equations and systems with randomness (34F05) Asymptotic properties of solutions to ordinary differential equations (34D05)

Related Items (9)

Lyapunov exponents for small random perturbations of Hamiltonian systems. ⋮ LYAPUNOV EXPONENTS AND RESONANCE FOR SMALL PERIODIC AND RANDOM PERTURBATIONS OF A CONSERVATIVE LINEAR SYSTEM ⋮ Stochastic stability of three-dimensional linear systems under parametric random action ⋮ Lyapunov exponent and rotation number of a two-dimensional nilpotent stochastic system ⋮ Almost sure and moment Lyapunov exponents for a stochastic beam equation ⋮ Positive Lyapunov exponent in the Hopf normal form with additive noise ⋮ Lyapunov exponents of nilpotent ito systems ⋮ Stochastic averaging and asymptotic behavior of the stochastic Duffing--van der Pol equation ⋮ Orbital stability index for stochastic systems

Cites Work

• Zur Umkehrbarkeit der statistischen Naturgesetze
• On the Behavior of the Invariant Measure of a Diffusion Process with Small Diffusion on a Circle
• Behavior of a linear system under small random excitation of its parameters
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