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 $\mathrm{\parallel }\cdot {\mathrm{\parallel }}_{L^p((0,T)\times \mathrm{\Omega };L^q(\mathcal{O}))}$, $p,q\in [2,\mathrm{\infty })$, is derived via a duality argument.