Extremes of Gaussian and non-Gaussian vector processes: a geometric approach

An alternative approach to direct application of the out-crossing rate for Gaussian and non-Gaussian vector processes is considered. Multivariate extreme-value distributions are established, and the properties of these distributions are investigated. The feasibility of the "expected extreme" ellipsoids are considered for the same categories of vector-processes in relation to load combination problems. Focus is presently on two-dimensional vector processes, but higher-dimensional extensions are also established. Examples of extreme hyper-ellipsoids in three dimensions are presented for both Gaussian and non-Gaussian processes. (C) 2003 Elsevier Ltd. All rights reserved.