Algebraic models for Gaussian measures on Banach spaces

1976 ◽  
pp. 53-65 ◽  
Author(s):  
Mark J. Christensen ◽  
A. T. Bharucha-Reid
Keyword(s):  
Banach Spaces ◽  
Gaussian Measures ◽  
Algebraic Models

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.

Algebraic models for probability measures on Banach spaces

1976 ◽  
Vol 8 (2) ◽  
pp. 215-217
Author(s):  
A. T. Bharucha-Reid
Keyword(s):  
Banach Spaces ◽  
Probability Measures ◽  
Algebraic Models

Invariant Gaussian measures for operators on Banach spaces and linear dynamics

2006 ◽  
Vol 94 (1) ◽  
pp. 181-210 ◽  
Author(s):  
Frédéric Bayart ◽  
Sophie Grivaux
Keyword(s):  
Banach Spaces ◽  
Gaussian Measures ◽  
Linear Dynamics

The Support of Gaussian Measures on Banach Spaces

1973 ◽  
Vol 17 (4) ◽  
pp. 728-734 ◽  
Author(s):  
Balram S. Rajput
Keyword(s):  
Banach Spaces ◽  
Gaussian Measures
Sign in / Sign up

Export Citation Format

Share Document