Asymptotic Stability of Nonlinear Stochastic Evolution Equations

DOI10.1081/SAP-120019288zbMath1055.60065MaRDI QIDQ4799710

José Real, Tomás Caraballo Garrido, María J. Garrido-Atienza

Publication date: 25 March 2003

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

zbMATH Keywords

stochastic evolution equationsgeneral decay ratesstochastic delay evolution equationsalmost sure asymptotic stability

Mathematics Subject Classification ID

Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) Asymptotic stability in control theory (93D20) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Infinite-dimensional random dynamical systems; stochastic equations (37L55)

Related Items (13)

Practical stability of stochastic delay evolution equations ⋮ ‐stability of hybrid neutral stochastic differential equations with infinite delay ⋮ Stability with respect to a part of the variables of stochastic nonlinear systems driven by G-Brownian motion ⋮ Practical stability with respect to a part of the variables of stochastic differential equations driven by G-Brownian motion ⋮ Unnamed Item ⋮ Stability of delay evolution equations with stochastic perturbations ⋮ Stability with general decay rates of stochastic differential delay equations with Poisson jumps and Markovian switching ⋮ Practical Asymptotic Stability of Nonlinear Stochastic Evolution Equations ⋮ On the practical global uniform asymptotic stability of stochastic differential equations ⋮ Moment decay rates of infinite dimensional stochastic evolution equations with memory and Markovian jumps ⋮ The Exponential Behaviour of Nonlinear Stochastic Functional Equations of Second Order in Time ⋮ Partial stability analysis of stochastic differential equations with a general decay rate ⋮ Stability of delay evolution equations with fading stochastic perturbations

Cites Work

• Stability of semilinear stochastic evolution equations
• Asymptotic stability of the linear Ito equation in infinite dimensions
• On exponential stability criteria of stochastic partial differential equations
• Stochastic functional partial differential equations: existence, uniqueness and asymptotic decay property
• On stabilization of partial differential equations by noise
• Lyapunov functionals and asymptotic stability of stochastic delay evolution equations
• Necessary and Sufficient Conditions for Exponential Stability and Ultimate Boundedness of Systems Governed by Stochastic Partial Differential Equations
• EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR DELAY STOCHASTIC EVOLUTION EQUATIONS

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