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 ·_L^p((0,T)×Ω;L^q(𝒪)), p,q ∈ [2,∞), is derived via a duality argument.