Asymptotic crossing rate of Gaussian vector processes into intersections of failure domains

Abstract

By use of asymptotic analysis, the asymptotic rate of exits of Gaussian vector processes with continuously differentiable sample paths into intersections of failure domains with piecewise twice differentiable boundaries is derived. After some convenient orthogonal transformations, the result only involves local properties of the failure surface at the so-called Beta-point and the cross-correlation matrix between the process and its time-derivative.