Stability of nonlinear delay evolution equation with stochastic perturbations is considered. It is shown that if the level of stochastic perturbations fades on the infinity, for instance, if it is given by square integrable function, then an exponentially stable deterministic system remains to be exponentially stable (in mean square). Applications of the obtained results to stochastic reaction-diffusion equations and stochastic 2D Navier-Stokes model are shown.

中文翻译：

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具有随机衰减的时滞发展方程的稳定性。

考虑了具有随机扰动的非线性时滞演化方程的稳定性。结果表明，如果随机扰动的水平在无穷大处逐渐减小，例如，如果它是由平方可积函数给出的，那么一个指数稳定的确定性系统将保持指数稳定（均方）。显示了所得结果在随机反应扩散方程和随机二维Navier-Stokes模型中的应用。