  In this paper we consider the two-dimensional stochastic Gross-Pitaevskii
equation, which is a model to describe Bose-Einstein condensation at positive
temperature. The equation is a complex Ginzburg-Landau equation with a harmonic
potential and an additive space-time white noise. We study the well-posedness
of the model using an inhomogeneous Wick renormalization due to the potential,
and prove the existence of an invariant measure and of stationary martingale
solutions.
