DICHOTOMY SPECTRUM OF NONAUTONOMOUS LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS

DOI10.1142/S0219493702000364zbMath1034.34057OpenAlexW1976303691MaRDI QIDQ3149360

Stefan Siegmund, Nguyen Dinh Cong

Publication date: 23 April 2003

Published in: Stochastics and Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219493702000364

zbMATH Keywords

asymptotic stabilitystochastic differential equationsLyapunov spectrumdichotomy spectrumnonautonomous linear stochastic systemsqualitative properties of stochastic flowssample-wise exponential dichotomy

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) Asymptotic stability in control theory (93D20) Linear ordinary differential equations and systems (34A30) Ordinary differential equations and systems with randomness (34F05) Generation, random and stochastic difference and differential equations (37H10) Dichotomy, trichotomy of solutions to ordinary differential equations (34D09)

Related Items (8)

ALMOST ALL NONAUTONOMOUS LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS ARE REGULAR ⋮ Lyapunov regularity for random dynamical systems ⋮ Nonuniform dichotomy spectrum and reducibility for nonautonomous difference equations ⋮ Dynamical spectrum in random dynamical systems ⋮ A random dynamical systems perspective on stochastic resonance ⋮ A new method to prove the nonuniform dichotomy spectrum theorem in ℝⁿ ⋮ Nonuniform dichotomy spectrum and reducibility for nonautonomous equations ⋮ The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor

Cites Work

• A spectral theory for linear differential systems
• Perfect cocycles through stochastic differential equations
• Ergodic Properties of Linear Dynamical Systems
• LYAPUNOV SPECTRUM OF NONAUTONOMOUS LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS
• Dichotomy spectrum for nonautonomous differential equations

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