25 research outputs found
Asymptotic representations for solutions of a class of second order nonlinear differential equations
On Necessary and Sufficient Conditions for Preserving Convergence Rates to Equilibrium in Deterministically and Stochastically Perturbed Differential Equations with Regularly Varying Nonlinearity
This paper develops necessary and sufficient conditions for the preservation
of asymptotic convergence rates of deterministically and stochastically
perturbed ordinary differential equations with regularly varying nonlinearity
close to their equilibrium. Sharp conditions are also established which
preserve the asymptotic behaviour of the derivative of the underlying
unperturbed equation. Finally, necessary and sufficient conditions are
established which enable finite difference approximations to the derivative in
the stochastic equation to preserve the asymptotic behaviour of the derivative
of the unperturbed equation, even though the solution of the stochastic
equation is nowhere differentiable, almost surely