Maximal inequalities and space-time regularity of stochastic convolutions

summary:Space-time regularity of stochastic convolution integrals J = {\int^\cdot_0 S(\cdot-r)Z(r)W(r)} driven by a cylindrical Wiener process $W$ in an $L^2$-space on a bounded domain is investigated. The semigroup $S$ is supposed to be given by the Green function of a $2m$-th order parabolic boundary value problem, and $Z$ is a multiplication operator. Under fairly general assumptions, $J$ is proved to be Holder continuous in time and space. The method yields maximal inequalities for stochastic convolutions in the space of continuous functions as well