The effect of additive fading stochastic perturbations of the type of white noise and Poisson’s jumps on an exponentially $p$-stable zero solution of a stochastic delay differential equation is studying. Condition on the rate of perturbations fading is obtained by which the solution of the perturbed stochastic delay differential equation remains asymptotically $p$-trivial. The obtained conditions are formulated in the terms of Lyapunov functionals and linear matrix inequalities (LMIs) and are demonstrated by some illustrative examples with numerical simulation.

中文翻译：

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具有加性衰落摄动的随机时滞微分方程解的性质

白噪声类型的加性衰落随机扰动和泊松跳跃的影响呈指数级 $p$随机时滞微分方程的稳定零解研究。获得扰动衰减率的条件，通过该条件渐进地保持扰动的随机时滞微分方程的解。$p$-不重要的。根据Lyapunov泛函和线性矩阵不等式（LMI）来公式化所获得的条件，并通过一些数值模拟的说明性例子加以证明。