Explicit Karhunen-Loève expansions related to the Green function of the Laplacian

Tom 72 / 2006

J.-R. Pycke Banach Center Publications 72 (2006), 263-270 MSC: 62G10, 62E20. DOI: 10.4064/bc72-0-17

Streszczenie

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.

Autorzy

  • J.-R. PyckeL.S.T.A, Jean-Renaud Pycke
    Université Paris VI
    case 158
    175 rue du Chevaleret
    75013 Paris, France
    e-mail

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