Non-Gaussianity of invariant measures to SPDEs in Da Prato-Debussche regime

2025/01/11 by Chandra, Ajay, Chevyrev, Ilya · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2501.06612

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 Φ⁴_δ 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.

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• On the Onsager-Machlup functional of the Φ⁴-measure

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