For the Euler scheme of the stochastic linear evolution equations, discrete stochastic maximal $ L^p $-regularity estimate is established, and a sharp error estimate in the norm $ \|\cdot\|_{L^p((0,T)\times\Omega;L^q(\mathcal O))} $, $ p,q \in [2,\infty) $, is derived via a duality argument.

翻译：针对随机线性演化方程的Euler格式，建立了离散随机极大$L^p$-正则性估计，并通过对偶论证推导出在范数$\|\cdot\|_{L^p((0,T)\times\Omega;L^q(\mathcal O))}$（$p,q \in [2,\infty)$）下的最优误差估计。