On Necessary and Sufficient Conditions for Preserving Convergence Rates to Equilibrium in Deterministically and Stochastically Perturbed Differential Equations with Regularly Varying Nonlinearity

DOI10.1007/978-3-319-08251-6_1zbMath1322.34063arXiv1409.1024OpenAlexW2120427285MaRDI QIDQ5259807

John A. D. Appleby, Denis D. Patterson

Publication date: 29 June 2015

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.1024

zbMATH Keywords

regular variationasymptotic stabilitystochastic differential equationsdifferential equationsglobal asymptotic stabilityfading perturbationstate-independent diffusion

Mathematics Subject Classification ID

Stability of solutions to ordinary differential equations (34D20) Perturbations of ordinary differential equations (34D10) Ordinary differential equations and systems with randomness (34F05) Asymptotic properties of solutions to ordinary differential equations (34D05) Rate of growth of functions, orders of infinity, slowly varying functions (26A12)

Related Items (2)

Growth rates of solutions of superlinear ordinary differential equations ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic behavior of one class of solutions of nonlinear nonautonomous second-order differential equations
• Asymptotic representations of solutions of nonautonomous ordinary differential equations with regularly varying nonlinearities
• Polynomial stability for perturbed stochastic differential equations with respect to semimartingales
• Exponential stability of non-linear stochastic evolution equations
• Regular variation and differential equations
• Characterisation of the asymptotic behaviour of scalar linear differential equations with respect to a fading stochastic perturbation
• A constructive comparison technique for determining the asymptotic behaviour of linear functional differential equations with unbounded delay
• Pathwise non-exponential decay rates of solutions of scalar nonlinear stochastic differential equations
• On exact rates of decay of solutions of linear systems of Volterra equations with delay
• Perturbation theorems for ordinary differential equations
• SOME REMARKS ON EXPONENTIAL STABILITY OF STOCHASTIC DIFFERENTIAL EQUATIONS
• LARGE TIME DECAY BEHAVIOR OF DYNAMICAL EQUATIONS WITH RANDOM PERTURBATION FEATURES
• On the Almost Sure Running Maxima of Solutions of Affine Stochastic Functional Differential Equations
• On exact convergence rates for solutions of linear systems of Volterra difference equations†
• ALMOST SURE POLYNOMIAL STABILITY FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS
• Weak exponential stability of stochastic differential equations
• Classification of convergence rates of solutions of perturbed ordinary differential equations with regularly varying nonlinearity
• On asymptotic stability and instability with respect to a fading stochastic perturbation
• On asymptotically autonomous differential equations

This page was built for publication: On Necessary and Sufficient Conditions for Preserving Convergence Rates to Equilibrium in Deterministically and Stochastically Perturbed Differential Equations with Regularly Varying Nonlinearity