This paper is concerned with the global attracting sets and the exponential stability in the mean square of mild solutions for stochastic functional partial differential equations. Some new sufficient conditions ensuring the existence of the global attracting sets and the exponential stability in the mean square of mild solutions for the considered equations are established by introducing approximating systems with strong solutions and using a limiting argument. Finally, some examples are investigated to illustrate the theory.

中文翻译：

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随机偏泛函微分方程的全局吸引集和指数稳定性

本文研究了随机泛函偏微分方程的温和解的均值平方的全局吸引集和指数稳定性。通过引入具有强解的近似系统并使用一个限制参数，建立了一些新的充分条件，确保了存在全局吸引集和所考虑方程的温和解均方的指数稳定性。最后，研究了一些例子来说明这一理论。