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

TL;DR

This paper establishes stability, convergence, and error estimates for the Euler scheme applied to stochastic linear evolution equations in Banach spaces, advancing numerical analysis in stochastic PDEs.

Contribution

It provides the first discrete stochastic maximal regularity estimate and a sharp error bound for the Euler scheme in Banach space settings.

Findings

Discrete stochastic maximal $L^p$-regularity estimate proved

Sharp error estimate derived in $L^p$-norm

Results applicable to stochastic PDEs 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 $ \|\cdot\|_{L^p((0,T)\times\Omega;L^q(\mathcal O))} $, $ p,q \in [2,\infty) $, is derived via a duality argument.