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December, 1972 Gaussian Processes and Gaussian Measures
Balram S. Rajput, Stamatis Cambanis
Ann. Math. Statist. 43(6): 1944-1952 (December, 1972). DOI: 10.1214/aoms/1177690865

Abstract

The subject of this paper is the study of the correspondence between Gaussian processes with paths in linear function spaces and Gaussian measures on function spaces. For the function spaces $C(I), C^n\lbrack a, b\rbrack, AC\lbrack a, b\rbrack$ and $L_2(T, \mathscr{A}, \nu)$ it is shown that if a Gaussian process has paths in these spaces then it induces a Gaussian measure on them, and, conversely, that every Gaussian measure on these spaces is induced by a Gaussian process with paths in these spaces.

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Balram S. Rajput. Stamatis Cambanis. "Gaussian Processes and Gaussian Measures." Ann. Math. Statist. 43 (6) 1944 - 1952, December, 1972. https://doi.org/10.1214/aoms/1177690865

Information

Published: December, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0255.60004
MathSciNet: MR370728
Digital Object Identifier: 10.1214/aoms/1177690865

Rights: Copyright © 1972 Institute of Mathematical Statistics

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Vol.43 • No. 6 • December, 1972
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