具有规则变化非线性的确定性随机扰动微分方程保持平衡点收敛速度的充要条件
On Necessary and Sufficient Conditions for Preserving Convergence Rates to Equilibrium in Deterministically and Stochastically Perturbed Differential Equations with Regularly Varying Nonlinearity
摘要：
本文给出了确定性和随机扰动的非线性项在平衡点附近正则变化的常微分方程保持渐近收敛速度的充要条件。尖锐的条件也建立保持的基本未扰动方程的衍生物的渐近行为。最后，建立了充要条件，使有限差分近似的随机方程的导数保持渐近行为的未扰动方程，即使随机方程的解决方案是无处可微，几乎肯定。
英文摘要：
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.
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