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Non-Gaussianity of invariant measures to SPDEs in Da Prato-Debussche regime
1Imperial College London, London, England.
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 measures in dimensions , which includes cases where the invariant measure is singular with respect to the invariant measure of the linear solution.
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