Abstract
Conditions under which samples of continuous stochastic processes X(t) on bounded time intervals [0,τ] can be represented by samples of finite dimensional (FD) processes Xd(t) are augmented such that samples of Slepian models Sd,a(t) of Xd(t) can be used as surrogates for samples of Slepian models Sa(t) of X(t). FD processes are deterministic functions of time and d<∞ random variables. The discrepancy between target and FD samples is quantified by the metric of the space C[0,τ] 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.
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