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

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.