I'm reading Hairer's notes on SPDEs: http://www.hairer.org/notes/SPDEs.pdf
He says on page 6 that "the stationary solution to the stochastic heat equation is Gaussian free field". He never defines what "stationary solution" means and it's not obvious. Does it mean that the solution doesn't depend on time? Since the noise depends on time this can never happen.
What is the stationary solution to a SPDE?