Spatial ergodicity for SPDEs via Poincaré-type inequalities

Le Chen, Davar Khoshnevisan, David Nualart +1

Consider a parabolic stochastic PDE of the form ${\partial }_{t}u=\frac{1}{2}\Delta u+\sigma (u)\eta$, where $u=u(t,x)$ for $t\ge 0$ and $x\in {\mathbb{R}}^d$, $\sigma :\mathbb{R}\to \mathbb{R}$ is…