LARGE TIME DECAY BEHAVIOR OF DYNAMICAL EQUATIONS WITH RANDOM PERTURBATION FEATURES

DOI10.1081/SAP-100001190zbMath0997.93095OpenAlexW2045921245MaRDI QIDQ2746370

Kai Liu, Xuerong Mao

Publication date: 4 November 2002

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

Full work available at URL: https://doi.org/10.1081/sap-100001190

zbMATH Keywords

stochastic differential equationtime delayperturbationdecay functionsalmost sure stability

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Perturbations in control/observation systems (93C73) Asymptotic stability in control theory (93D20) Robust stability (93D09) Stochastic stability in control theory (93E15) Stochastic functional-differential equations (34K50)

Related Items (13)

Practical stability of stochastic delay evolution equations ⋮ The Razumikhin approach on general decay stability for neutral stochastic functional differential equations ⋮ Razumikhin-type theorems on general decay stability of stochastic functional differential equations with infinite delay ⋮ Non-exponential stability of scalar stochastic Volterra equations. ⋮ On pathwise super-exponential decay rates of solutions of scalar nonlinear stochastic differential equations ⋮ Stochastic stability of a class of unbounded delay neutral stochastic differential equations with general decay rate ⋮ Stability with general decay rates of stochastic differential delay equations with Poisson jumps and Markovian switching ⋮ Practical Asymptotic Stability of Nonlinear Stochastic Evolution Equations ⋮ Robustness of general decay stability of nonlinear neutral stochastic functional differential equations with infinite delay ⋮ Stochastic stabilization of differential systems with general decay rate ⋮ The asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Lévy noise ⋮ Moment decay rates of infinite dimensional stochastic evolution equations with memory and Markovian jumps ⋮ On Necessary and Sufficient Conditions for Preserving Convergence Rates to Equilibrium in Deterministically and Stochastically Perturbed Differential Equations with Regularly Varying Nonlinearity

Cites Work

• Random differential inequalities
• Stability of nonlinear stochastic-evolution equations
• Stability of semilinear stochastic evolution equations
• Asymptotic stability of the linear Ito equation in infinite dimensions
• On stability for a class of semilinear stochastic evolution equations
• Stabilization of Linear Systems by Noise
• Asymptotic stability and spiraling properties for solutions of stochastic equations
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