Non-Gaussianity of invariant measures to SPDEs in Da Prato–Debussche regime
File(s)
Published version
Author(s)
Chandra, Ajay
Chevyrev, Ilya
Type
Journal Article
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 4δ 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.
Date Issued
2025-03-01
Date Acceptance
2025-06-02
Citation
Stochastics and Partial Differential Equations: Analysis and Computations, 2025, 14 (1), pp.323-349
ISSN
2194-0401
Publisher
Springer Science and Business Media LLC
Start Page
323
End Page
349
Journal / Book Title
Stochastics and Partial Differential Equations: Analysis and Computations
Volume
14
Issue
1
Copyright Statement
© The Author(s) 2025 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
10.1007/s40072-025-00370-3
Subjects
Stochastic PDEs
Da Prato-Debussche
Invariant measure
Markov process
Euclidean field theory
Publication Status
Published
Date Publish Online
2025-06-19