Stability and convergence of the Euler scheme for stochastic linear evolution equations in Banach spaces

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.