Concentration estimates for slowly time-dependent singular SPDEs on the two-dimensional torus. (English) Zbl 1540.60141
This article focuses on 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. The main results are the Wick powers of the stochastic convolution remain concentrated, with high probability, in a neighborhood of a stable equilibrium branch of the equation without noise, measured in appropriate Besov and Hölder norms. The authors also discuss the particular situation of a dynamic pitchfork bifurcation. These results extend to the two-dimensional torus those obtained in [N. Berglund and B. Gentz, Probab. Theory Relat. Fields 122, No. 3, 341–388 (2002; Zbl 1008.37031)] for finite-dimensional SDEs, and in [N. Berglund and R. Nader, Stoch. Partial Differ. Equ., Anal. Comput. 11, No. 1, 348–387 (2023; Zbl 1517.60072)] for SPDEs on the one-dimensional torus.
Reviewer: Guanggan Chen (Chengdu)
MSC:
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 60G17 | Sample path properties |
| 34F15 | Resonance phenomena for ordinary differential equations involving randomness |
| 37H20 | Bifurcation theory for random and stochastic dynamical systems |
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