Finite dimensional models for extremes of Gaussian and non-Gaussian processes

Numerical solutions of stochastic problems involving random processes X(t), which constitutes infinite families variables, require to represent these by finite dimensional (FD) models Xd(t), i.e., deterministic functions time depending on numbers d variables. Most available FD match the mean, correlation, and other global properties X(t). They provide useful information a broad range problems, but cannot be used estimate extremes or sample We develop Xd(t) for X(t) with continuous samples establish conditions under converge weakly in space as d→∞. These theoretical results are illustrated numerical examples show that, established this study, can approximated that discrepancy between decreases d.