The Karhunen-Loève Expansion gives an optimal series representation of random fields using eigenfunctions of the covariance operator, with analysis of convergence and computational aspects.
Lifshits , Lectures on Gaussian Processes , Springer
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A Primer on the Karhunen-Lo\`eve Expansion
The Karhunen-Loève Expansion gives an optimal series representation of random fields using eigenfunctions of the covariance operator, with analysis of convergence and computational aspects.