Abstract
We consider a sequence of Gaussian tensor product-type random fields Open image in new window , where Open image in new window and Open image in new window are all positive eigenvalues and eigenfunctions of the covariance operator of the process X1, Open image in new window are standard Gaussian random variables, and Open image in new window is a subset of positive integers. For each d ∈ ℕ, the sample paths of Xd almost surely belong to L2([0, 1]d) with norm ∥·∥2,d. The tuples Open image in new window, are the eigenpairs of the covariance operator of Xd. We approximate the random fields Xd, d ∈ Open image in new window, by the finite sums Xd(n) corresponding to the n maximal eigenvalues λk, Open image in new window.
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