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

Abstract

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 $\Vert \cdot {\Vert }_{L^p((0,T)\times \hat{I}\text{c◯};L^q(\mathcal{O}))}$, $p,q\in [2,\infty )$, is derived via a duality argument.