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A
characterization of the Gaussian distribution in a Hilbert
space
Jeffrey Lynn Spielman |
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Vol. 68 (1977), No. 2, 497–505
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Abstract |
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In this paper we consider the case in which random variables Xj take values in a real, separable Hilbert space ℋ. We look at a linear form ∑ AjXj where each Aj is a bounded linear operator in ℋ. We then assume that this linear form is identically distributed with a monomial and form conditions under which it is possible to deduce that the common distribution of the random variables is the Gaussian distribution. |
Mathematical Subject Classification 2000
Primary: 60B05
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Milestones
Received: 2 April 1976
Published: 1 February 1977
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Authors |
| Jeffrey Lynn Spielman | |
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