Concentration estimates for slowly time-dependent singular SPDEs on the two-dimensional torus
arXiv:2209.15357 · doi:10.1214/24-EJP1094
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 [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.
arXiv comment36 pages. Typos corrected, additional details in 2 proofs
References in corpus (14)
- A theory of regularity structures
- Renormalising SPDEs in regularity structures
- A mathematical framework for critical transitions: normal forms, variance and applications
- Geometric singular perturbation theory for stochastic differential equations
- Large deviations for white-noise driven, nonlinear stochastic PDEs in two and three dimensions
- Pathwise description of dynamic pitchfork bifurcations with additive noise
- Sharp estimates for metastable lifetimes in parabolic SPDEs: Kramers' law and beyond
- A solution theory for quasilinear singular SPDEs
- The effect of additive noise on dynamical hysteresis
- An Eyring-Kramers law for the stochastic Allen-Cahn equation in dimension two
- A sample-paths approach to noise-induced synchronization: Stochastic resonance in a double-well potential
- Ergodicity for the stochastic quantization problems on the 2D-torus
- Stochastic resonance in stochastic PDEs
- Boundary renormalisation of SPDEs