Invariant measures for stochastic heat equations with unbounded coefficients

The paper deals with the Cauchy problem in of a stochastic heat equation . The locally lipschitz drift coefficient f can have polynomial growth while the diffusion coefficient [sigma] is supposed to be lipschitz but not necessarily bounded. Of course, for the existence of a solution alone, a certain dissipativity of f is needed. Applying the comparison method, a condition on the strength of this dissipativity is derived even ensuring the existence of an invariant measure.