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arxiv: 1509.07526 · v2 · submitted 2015-09-24 · 🧮 math.PR

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A brief note on the Karhunen-Lo\`eve expansion

Alen Alexanderian
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classification 🧮 math.PR
keywords expansionkarhunen-lobriefbrieflyderivationdetaileddiscussgaussian
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We provide a detailed derivation of the Karhunen-Lo\`eve expansion of a stochastic process. We also discuss briefly Gaussian processes, and provide a simple numerical study for the purpose of illustration.

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  1. A Primer on the Karhunen-Lo\`eve Expansion

    math.NA 2026-05 unverdicted novelty 2.0

    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.