In this paper, we investigate the stochastic evolution equations (SEEs) driven by $\log$-Whittle-Mat$\acute{{\mathrm{e}}}$rn (W-M) random diffusion coefficient field and $Q$-Wiener multiplicative force noise. First, the well-posedness of the underlying equations is established by proving the existence, uniqueness, and stability of the mild solution. A sampling approach called approximation circulant embedding with padding is proposed to sample the random coefficient field. Then a spatio-temporal discretization method based on semi-implicit Euler-Maruyama scheme and finite element method is constructed and analyzed. An estimate for the strong convergence rate is derived. Numerical experiments are finally reported to confirm the theoretical result.

翻译：在本文中,我们研究了由 $\log$-Witle-Mat$\acute ⁇ mathrm{e ⁇ $rn (W-M) 随机扩散系数字段和 $Q-Winer 倍增效应噪音驱动的随机进化方程式(SEE) 。 首先, 基础方程式的准确性是通过证明温度溶液的存在、 独特性和稳定性来确定的。 提议了一种叫作近似环球嵌入垫板的抽样方法来抽样随机系数字段。 然后根据半隐含的极光- 海洋方案和有限元素方法构建并分析一个时分解法。 得出了强集率的估计值。 最终报告了数值实验以证实理论结果。