Asymptotic crossing rates for stationary Gaussian vector processes (Q1105278)

The expected number of crossings of a differentiable Gaussian vector process through a hypersurface is given by a surface integral over this surface. Simple asymptotic approximations for these integrals are derived. The results are obtained by a generalization of the Laplace method for the asymptotic expansion of multidimensional integrals. With these formulas approximations for the extreme value distribution of functions of vector processes can be found.