The asymptotic stability and exponential stability of nonlinear stochastic differential systems with Markovian switching and with polynomial growth

DOI10.1016/j.jmaa.2012.01.058zbMath1238.93118OpenAlexW2082280992MaRDI QIDQ413249

Yi Shen, Lei Liu

Publication date: 4 May 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.01.058

zbMATH Keywords

exponential stabilityBrownian motionasymptotic stabilityItô's formulasemi-martingale convergence theoremMarkovian chain

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Asymptotic stability in control theory (93D20) Stochastic stability in control theory (93E15)

Related Items (10)

Stability of nonlinear stochastic Markov jump system with mode-dependent delays and applications ⋮ Stabilization of stochastic regime-switching Poisson jump equations by delay feedback control ⋮ Robust stability of a class of stochastic functional differential equations with Markovian switching ⋮ Improved Razumikhin and Krasovskii stability criteria for time-varying stochastic time-delay systems ⋮ Verification theory and approximate optimal harvesting strategy for a stochastic competitive ecosystem subject to Lévy noise ⋮ Stability analysis for stochastic differential equations with infinite Markovian switchings ⋮ On the detectability and observability of continuous stochastic Markov jump linear systems ⋮ A note on stability of hybrid stochastic differential equations ⋮ The stability with a general decay of stochastic delay differential equations with Markovian switching ⋮ Asymptotic stability of nonlinear hybrid stochastic systems driven by linear discrete time noises

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