STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS: ANALYSIS AND COMPUTATIONS
Abstract
We propose an elementary method to show non-Gaussianity of invariant measures of parabolic stochastic partial differential equations with polynomial non-linearities in the Da Prato–Debussche regime. The approach is essentially algebraic and involves using the generator equation of the SPDE at stationarity. Our results in particular cover the Φδ4 measures in dimensions δ<14/5, which includes cases where the invariant measure is singular with respect to the invariant measure of the linear solution.
