A characterization of Gaussian law in Hilbert space (Q809462)
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scientific article; zbMATH DE number 4213111
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of Gaussian law in Hilbert space |
scientific article; zbMATH DE number 4213111 |
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A characterization of Gaussian law in Hilbert space (English)
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1991
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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.
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Gaussian law in Hilbert space
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characteristic functions
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