Special Session 11: Stochastic Partial Differential Equations

Concentration results for time-dependent SPDEs with Gaussian and fractional noise
Nils Berglund
IDP, University of Orleans
France
Co-Author(s):    Alexandra Blessing, Rita Nader
Abstract:
We consider slowly time-dependent parabolic SPDEs on the torus of dimension $1$ or $2$, driven by either Gaussian, or by fractional space-time white noise with Hurst parameter strictly above $1/4$. We obtain concentration estimates for solutions near stable critical curves of these equations. As an application, we prove a quantitative result on stochastic resonance for periodically forced SPDEs. References: 1. NB, Rita Nader, Stochastic resonance in stochastic PDEs, Stochastics and Partial Differential Equations: Analysis and Computations, 11:348-387 (2023). 2. NB, Rita Nader, Concentration estimates for slowly time-dependent singular SPDEs on the two-dimensional torus, Electronic J. Probability 29:1-35 (2024). 3. NB, Alexandra Blessing (Neamtu), Concentration estimates for SPDEs driven by fractional Brownian motion Electron. Commun. Probab. 30:1-13 (2025).