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

Abstract

Stochastic partial differential equations on ℝd 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 Lq-space. Then we obtain the existence of a space continuous solution by means of the Da Prato, Kwapień and Zabczyk factorization identity for stochastic convolutions.