Space-time continuous solutions to SPDE's driven by a homogeneous Wiener process
Volume 137 / 1999
Studia Mathematica 137 (1999), 261-299
DOI: 10.4064/sm-137-3-261-299
Abstract
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 Prato, Kwapień and Zabczyk factorization identity for stochastic convolutions.
