The ergodic theory of SPDEs in a weak-noise regime

Mathew Joseph, Davar Khoshnevisan, Kunwoo Kim +1

Consider a parabolic SPDE \[ \partial_t u = Δu + σ(u)η, \] on $(0,\infty )\times {\mathbb{R}}^d$, where $\eta$ is a centered, generalized Gaussian noise with $\text{Cov}[η(t\,,x)\,,η(s\…