Evaluation of Karhunen–Loève, Spectral, and Sampling Representations for Stochastic Processes

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Simulation of simply cross correlated random fields by series expansion methods (2008, methodology): “The univariate nonlinear transformation of the Gaussian variables, called the translation process by Grigoriu [2] is the mapping hi(·): H̃i (xk) = hi [Hi (xk)] = G −1 i {Φ [Hi (xk)]} (13) where Φ (·) is the standard cumulative Gaussian probability function and i = 1, . . . , NF ; k = 1, . . . , N .”
Karhunen-Loève expansion for multi-correlated stochastic processes (2013, methodology): “The series can be constructed, e.g., by using orthogonal polynomials [1] [2], spectral density methods [3] [4] [5] [6], wavelets [7] [8] [9], Karhunen–Loève (KL) decompositions [10] [11] [12] [13] [14] [15] [16], bi-orthogonal techniques [17] [18] [19] or functional principal component analyses…”