This paper studies the (random) uniform attractor for a class of non-autonomous stochastic evolution equations driven by a time-periodic forcing and multiplicative fractional noise with Hurst parameter bigger than 1/2. We first establish the existence and uniqueness results for the solution to the considered equation and show that the solution generates a jointly continuous non-autonomous random dynamical system (NRDS). Moreover, we prove the existence of the uniform attractor for this NRDS through stopping time technique. Particularly, a compact uniformly absorbing set is constructed under a smallness condition imposed on the fractional noise.

中文翻译：

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一类具有乘性分数噪声的随机演化方程的均匀吸引子

本文研究了由时间周期强迫和Hurst参数大于1/2的乘性分数噪声驱动的一类非自治随机演化方程的（随机）均匀吸引子。我们首先建立了所考虑方程解的存在性和唯一性结果，并表明该解生成了一个联合连续的非自治随机动力系统（NRDS）。此外，我们通过停止时间技术证明了该NRDS的均匀吸引子的存在。特别是，在对分数噪声施加较小的条件下构造了一个紧凑的均匀吸收集。