Extreme values and crossings for the chi^2-process and othe functions of multidimensional Gaussian processes, with reliability applications
Extreme values of non-linear functions of multivariate Gaussian processes are of considerable interest in engineering sciences dealing with the safety of structures. One then seeks the survival probability P{(X1(t),⋯ ,Xn(t))∈ S, all t∈ [0,T]}, where X(t)=(X1(t),⋯ ,Xn(t)) is a stationary, multivariate Gaussian load process, and S is a safe region. In general, the asymptotic survival probability for