Stability of an autonomous dynamic system with fast Markov switching

DOI10.1007/BF01089209zbMath0757.60051MaRDI QIDQ5896632

Vladimir S. Korolyuk

Publication date: 1991

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

stationary distributionLyapunov's functionaveraging systemasymptotic stability problemergodic Markov disturbances

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic stability in control theory (93E15) Averaging method for ordinary differential equations (34C29)

Related Items (10)

Stability of solutions of dynamic systems with randomly structured aftereffect ⋮ Asymptotic behavior of solutions of pulse systems with small parameter and Markov switchings. I: Uniform boundedness of solutions ⋮ Stability of semi-Markov evolution systems and its application in financial mathematics ⋮ Stability in impulsive systems with Markov perturbations in averaging scheme. II. Averaging principle for impulsive Markov systems and stability analysis based on averaged equations ⋮ Stability in impulsive systems with Markov perturbations in averaging scheme. III: Weak convergence of solutions of impulsive systems ⋮ Asymptotics of the state vector of delayed impulsive diffusion systems with Markov parameters ⋮ Stability of diffusion stochastic functional differential equations with Markov parameters ⋮ Stability in impulsive systems with Markov perturbations in averaging scheme. I: Averaging principle for impulsive Markov systems ⋮ Lyapunov function method for investigation of stability of stochastic Itô random-structure systems with impulse Markov switchings. I: General theorems on the stability of stochastic impulse systems ⋮ Lyapunov function method for investigation of stability of stochastic Ito random-structure systems with impulse Markov switchings. II: First-approximation stability of stochastic impulse systems with Markov parameters

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