A brief note on the Karhunen-Lo\`eve expansion
Alen Alexanderian
TL;DR
This paper offers a detailed derivation of the Karhunen-Loève expansion for stochastic processes, discusses Gaussian processes briefly, and includes a simple numerical example to illustrate the concepts.
Contribution
It provides a comprehensive derivation of the Karhunen-Loève expansion and includes an illustrative numerical study, enhancing understanding of the topic.
Findings
Derivation of the Karhunen-Loève expansion
Brief discussion on Gaussian processes
Numerical illustration of the expansion
Abstract
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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Taxonomy
TopicsMathematical Dynamics and Fractals · Functional Equations Stability Results · Geometric Analysis and Curvature Flows