Skip to Main content Skip to Navigation

Karhunen-Loève decomposition of Gaussian measures on banach spaces *

Abstract : The study of Gaussian measures on Banach spaces is of active interest both in pure and applied mathematics. In particular, the spectral theorem for self-adjoint compact operators on Hilbert spaces provides a canonical decomposition of Gaussian measures on Hilbert spaces, the so-called 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 to Gaussian measures on Banach spaces. In the special case of the standard Wiener measure, this decomposition matches with Lévy-Ciesielski construction of Brownian motion.
Document type :
Journal articles
Complete list of metadatas

https://hal-emse.ccsd.cnrs.fr/emse-02438500
Contributor : Florent Breuil <>
Submitted on : Tuesday, January 14, 2020 - 11:40:10 AM
Last modification on : Wednesday, March 4, 2020 - 12:28:05 PM

Links full text

Identifiers

Citation

Xavier Bay, Jean-Charles Croix. Karhunen-Loève decomposition of Gaussian measures on banach spaces *. Probability and Mathematical Statistics, 2019, 39 (2), pp.279-297. ⟨10.19195/0208-4147.39.2.3⟩. ⟨emse-02438500⟩

Share

Metrics

Record views

23