The expected Euler characteristic approximation to excursion probabilities of Gaussian vector fields

Dan Cheng, Yimin Xiao

Let $\{(X(t),Y(s)):t\in T,s\in S\}$ be an ${\mathbb{R}}^2$-valued, centered, unit-variance smooth Gaussian vector field, where $T$ and $S$ are compact rectangles in ${\mathbb{R}}^N$…