A characterization of Gaussian law in Hilbert space
Copyright policy )A characterization of Gaussian law in Hilbert space
Let \({\mathcal H}\) be a real separable Hilbert space and let X and Y be independent random variables taking values in \({\mathcal H}\). The aim of the paper is to prove that \(X+Y\) and X-Y are independent if and only if each of X and Y is Gaussian. The proof is based on solving a functional equation satisfied by the characteristic functions of X and Y.
- University System of Ohio United States
- Bowling Green State University United States
- DigiZeitschriften Germany
Gaussian law in Hilbert space, 510.mathematics, Infinitely divisible distributions; stable distributions, Functional equations for functions with more general domains and/or ranges, Characterizations of Hilbert spaces, Article, characteristic functions
Gaussian law in Hilbert space, 510.mathematics, Infinitely divisible distributions; stable distributions, Functional equations for functions with more general domains and/or ranges, Characterizations of Hilbert spaces, Article, characteristic functions
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