Finite dimensional (FD) Slepian models for non-Gaussian processes

Conditions under which samples of continuous stochastic processes X(t) on bounded time intervals [0, tau] can be represented by samples of finite dimensional (FD) processes X-d(t) are augmented such that samples of Slepian models S-d,S-a(t) of X-d(t) can be used as surrogates for samples of Slepian models of S-a(t) of X-d(t). FD processes are deterministic functions of time and d < infinity random variables. The discrepancy between target and FD samples is quantified by the metric of the space C[0, tau] of continuous functions. The numerical illustrations, which include Gaussian/non-Gaussian FD processes and solutions of linear/nonlinear random vibration problems, are consistent with the theoretical findings in the paper.