The mean Euler characteristic and excursion probability of Gaussian random fields with stationary increments

Dan Cheng, Yimin Xiao

Let $X=\{X(t),t\in {\mathbb{R}}^N\}$ be a centered Gaussian random field with stationary increments and $X(0)=0$. For any compact rectangle $T\subset {\mathbb{R}}^N$ and $u\in {\ma…