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)\timesΩ;L^q(\mathcal O))} $, $ p,q \in [2,\infty) $, is derived via a duality argument.
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