# On temporal regularity of stochastic convolutions in $2$-smooth Banach spaces

## TL;DR

This paper establishes that solutions to certain stochastic differential equations in 2-smooth Banach spaces exhibit temporal regularity comparable to Wiener processes, within a specific Besov-Orlicz space framework.

## Contribution

It demonstrates the temporal regularity of solutions in 2-smooth Banach spaces matches that of Wiener processes, extending current understanding in stochastic analysis.

## Key findings

- Solutions have the same temporal regularity as Wiener processes
- Regularity is characterized in the Besov-Orlicz space $B^{1/2}_{\Phi_2,\infty}$
- Applicable to parabolic stochastic differential equations

## Abstract

We show that paths of solutions to parabolic stochastic differential equations have the same regularity in time as the Wiener process (as of the current state of art). The temporal regularity is considered in the Besov-Orlicz space $B^{1/2}_{\Phi_2,\infty}(0,T;X)$ where $\Phi_2(x)=\exp(x^2)-1$ and $X$ is a $2$-smooth Banach space.