# Stability properties of stochastic maximal $L^p$-regularity

## TL;DR

This paper extends the theory of maximal $L^p$-regularity to stochastic evolution equations, demonstrating that key properties like independence of interval length, analyticity, and stability also hold in the stochastic setting.

## Contribution

It develops a stochastic maximal $L^p$-regularity theory paralleling Dore's deterministic results, establishing fundamental properties for stochastic evolution equations.

## Key findings

- Stochastic maximal $L^p$-regularity is independent of time interval length.
- Analyticity and exponential stability of semigroups are preserved in the stochastic setting.
- Stability under perturbation extends to stochastic evolution equations.

## Abstract

In this paper we consider $L^p$-regularity estimates for solutions to stochastic evolution equations, which is called stochastic maximal $L^p$-regularity. Our aim is to find a theory which is analogously to Dore's theory for deterministic evolution equations. He has shown that maximal $L^p$-regularity is independent of the length of the time interval, implies analyticity and exponential stability of the semigroup, is stable under perturbation and many more properties. We show that the stochastic versions of these results hold.