On Large Deviations of Gaussian Measures in Banach Spaces

1992 ◽  
pp. 228-244
Author(s):  
Marek Slaby
Keyword(s):  
Large Deviations ◽  
Banach Spaces ◽  
Gaussian Measures

scholarly journals Karhunen–Loève decomposition of Gaussian measures on Banach spaces

2019 ◽  
Vol 39 (2) ◽  
pp. 279-297
Author(s):  
Xavier Bay ◽  
Jean-Charles Croix
Keyword(s):  
Brownian Motion ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Applied Mathematics ◽  
Canonical Decomposition ◽  
Spectral Theorem ◽  
Gaussian Measures ◽  
Covariance Operators ◽  
Active Interest ◽  
Special Case

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 socalled Karhunen–Ločve 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.

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