The ergodic theory of SPDEs in a weak-noise regime
Abstract
Consider a parabolic SPDE on , where is a centered, generalized Gaussian noise with for a tempered Borel measure that is positive definite and satisfies a mild weak-noise. The existence of invariant measures of versions of these types of SPDEs has been studied at great length, particularly in the ``weak-noise regime''; see for example Assing and Manthey \cite{AssingManthey2003}, Chen and Eisenberg \cite{ChenEisenberg2024}, Chen, Ouyang, Tindel, and Xia \cite{ChenOuyangTindelXia2024}, Eckmann and Hairer \cite{EckmannHairer2001}, Misiats and Stanzhytskyi \cite{MSY2020}, Yu Gu and Jiawei Li \cite{GuLi2020}, and Tessitore and Zabczyk \cite{TessitoreZabczyk1998}. Here, we characterize all annealed, ergodic, invariant measures for the above SPDE in the weak-noise regime.
Cite
@article{arxiv.2603.18384,
title = {The ergodic theory of SPDEs in a weak-noise regime},
author = {Mathew Joseph and Davar Khoshnevisan and Kunwoo Kim and Carl Mueller},
journal= {arXiv preprint arXiv:2603.18384},
year = {2026}
}
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49 pages