Let $ {\cal T} (x,\varepsilon)$ denote the first hitting time of the disc of radius ε centered at ϰ for Brownian motion on the two dimensional torus T2. We prove that $\text {sup}_ {x\in {\Bbb T}^ {2} ...

We consider the wave equation in two spatial dimensions driven by space–time Gaussian noise that is white in time but has a nondegenerate spatial covariance. We give a necessary and sufficient ...