Delay differential equation is considered under stochastic perturbations of the type of white noise and Poisson's jumps. It is shown that if stochastic perturbations fade on the infinity quickly enough then sufficient conditions for asymptotic stability of the zero solution of the deterministic differential equation with delay provide also asymptotic mean square stability of the zero solution of the stochastic differential equation. Stability conditions are obtained via the general method of Lyapunov functionals construction and the method of Linear Matrix Inequalities (LMIs). Investigation of the situation when stochastic perturbations do not fade on the infinity or fade not enough quickly is proposed as an unsolved problem.

中文翻译：

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具有白噪声和泊松跳变的随机扰动的时滞微分方程的稳定性

在白噪声类型和泊松跳跃的随机扰动下，考虑了时滞微分方程。结果表明，如果随机扰动在无穷远处足够快地消失，则确定性微分方程零解的渐近稳定性的充分条件（具有延迟）也将提供随机微分方程零解的渐近均方稳定性。稳定性条件通过Lyapunov泛函构造的一般方法和线性矩阵不等式（LMI）的方法获得。随机扰动没有在无穷远处消失或没有足够快地消失的情况的研究被提出作为未解决的问题。