We study the spatial homogenisation of parabolic linear stochastic PDEs exhibiting a two-scale structure both at the level of the linear operator and at the level of the Gaussiandriving noise. We show that in some cases, in particular when the forcing is given by space time white noise, it may happen that the homogenised SPDE is not what one would expect from existing results for PDEs with more regular forcing terms.
"Stochastic PDEs with multiscale structure." Electron. J. Probab. 17 1 - 38, 2012. https://doi.org/10.1214/EJP.v17-1807