# Convergence of an operator splitting scheme for abstract stochastic evolution equations

## TL;DR

This paper proves that the Lie-Trotter operator splitting scheme for stochastic semi-linear evolution equations in a Hilbert space converges at the optimal half-order, depending on noise regularity, for both original and discretized problems.

## Contribution

It establishes the optimal convergence order of the Lie-Trotter splitting scheme in a general Hilbert space setting, accounting for noise regularity.

## Key findings

- Strong convergence order is half-order, which is optimal.
- Convergence applies to both original and spatially discretized problems.
- Order depends on the regularity of the noise.

## Abstract

In this paper we study the convergence of a Lie-Trotter operator splitting for stochastic semi-linear evolution equations in a Hilbert space. The abstract Hilbert space setting allows for the consideration of convergence of the approximation for both the original and spatially discretized problems. It is known that the strong convergence of this scheme is classically of half-order, at best. We demonstrate that this is in fact the optimal order of convergence in the proposed setting, with the actual order being dependent upon the regularity of noise collected from applications.