Karhunen-Loève expansions of Gaussian processes have numerous applications in Probability and Statistics. Unfortunately the set of Gaussian processes with explicitly known spectrum and eigenfunctions is narrow. An interpretation of three historical examples enables us to understand the key role of the Laplacian. This allows us to extend the set of Gaussian processes for which a very explicit Karhunen-Loève expansion can be derived.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-17,
author = {J.-R. Pycke},
title = {Explicit Karhunen-Lo\`eve expansions related to the Green function of the Laplacian},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {263-270},
zbl = {1105.60032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-17}
}
J.-R. Pycke. Explicit Karhunen-Loève expansions related to the Green function of the Laplacian. Banach Center Publications, Tome 72 (2006) pp. 263-270. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-17/