Karhunen-Loève Decomposition of Gaussian Measures on Banach Spaces

• Autorzy: Bay Xavier , Croix Jean-Charles

Identyfikatory

DOI

10.19195/0208-4147.39.2.3

• Języki publikacji: EN

Abstrakty

EN

The study of Gaussian measures on Banach spaces is of active interest both in pure and applied mathematics. In particular, the spectra theorem for self-adjoint compact operators on Hilbert spaces provides a canonical decomposition of Gaussian measures on Hilbert spaces, the socalled Karhunen-Loève expansion. In this paper, we extend this result to Gaussian measures on Banach spaces in a very similar and constructive manner. In some sense, this can also be seen as a generalization of the spectral theorem for covariance operators associated with Gaussian measures on Banach spaces. In the special case of the standardWiener measure, this decomposition matches with Lévy-Ciesielski construction of Brownian motion.

Słowa kluczowe

EN

Gaussian measure; covariance operator; orthogonal decomposition

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2019
• Tom: Vol. 39, Fasc. 2
• Strony: 279--297
• Opis fizyczny: Bibliogr. 18 poz., wykr.

Twórcy

autor

Bay Xavier

• Mines Saint-Étienne, Institut Fayol, Génie Mathématique et Industriel, LIMOS UMR 6158, 158 cours Fauriel, 42023 Saint-Étienne, France

autor

Croix Jean-Charles

• Mines Saint-Étienne, Institut Fayol, Génie Mathématique et Industriel, LIMOS UMR 6158, 158 cours Fauriel, 42023 Saint-Étienne, France

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).