Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process

Stochastic partial differential equations on R-d are considered. The noise is supposed to be a spatially homogeneous Wiener process. Using the theory of stochastic integration in Banach spaces we show the existence of a Markovian solution in a certain weighted L-q-space. Then we obtain the existence of a space continuous solution by means of the Da Prate, Kwapien and Zabczyk factorization identity for stochastic convolutions.