Abstract
We consider slowly time-dependent singular stochastic partial differential equations on the two-dimensional torus, driven by weak space-time white noise, and renormalised in the Wick sense. Our main results are concentration results on sample paths near stable equilibrium branches of the equation without noise, measured in appropriate Besov and Hölder norms. We also discuss a case involving a pitchfork bifurcation. These results extend to the two-dimensional torus those obtained in [4] for finite-dimensional SDEs, and in [9] for SPDEs on the one-dimensional torus.
Funding Statement
This work is supported by the ANR project PERISTOCH, ANR–19–CE40–0023.
Acknowledgments
The authors would like to thank Tom Klose for pointing out reference [27], and Dimitri Faure for pointing out several typos and a mistake in an earlier version of Remark 2.6. The authors also thank an anonymous referee for remarks that led to an improved presentation.
Citation
Nils Berglund. Rita Nader. "Concentration estimates for slowly time-dependent singular SPDEs on the two-dimensional torus." Electron. J. Probab. 29 1 - 35, 2024. https://doi.org/10.1214/24-EJP1094
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