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arXiv · 2501.06612

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

Ajay Chandra·Ilya Chevyrev
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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 $\Phi^4_\delta$ measures in dimensions $\delta<\frac{14}{5}$, which includes cases where the invariant measure is singular with respect to the invariant measure of the linear solution.

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Ajay Chandra, Ilya Chevyrev. 2025-01-11. Non-Gaussianity of invariant measures to SPDEs in Da Prato-Debussche regime. https://doi.org/10.1007/s40072-025-00370-3

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