Concentration estimates for slowly time-dependent singular SPDEs on the two-dimensional torus
Probability
2024-02-26 v2 Mathematical Physics
Analysis of PDEs
math.MP
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 H\"older norms. We also discuss a case involving a pitchfork bifurcation. These results extend to the two-dimensional torus those obtained in [Berglund and Gentz, Proability Theory and Related Fields, 2002] for finite-dimensional SDEs, and in [Berglund and Nader, Stochastics and PDEs, 2022] for SPDEs on the one-dimensional torus.
Cite
@article{arxiv.2209.15357,
title = {Concentration estimates for slowly time-dependent singular SPDEs on the two-dimensional torus},
author = {Nils Berglund and Rita Nader},
journal= {arXiv preprint arXiv:2209.15357},
year = {2024}
}
Comments
36 pages. Typos corrected, additional details in 2 proofs