Vol. 68, No. 2, 1977

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A characterization of the Gaussian distribution in a Hilbert space

Jeffrey Lynn Spielman

Vol. 68 (1977), No. 2, 497–505
Abstract

In this paper we consider the case in which random variables Xj take values in a real, separable Hilbert space . We look at a linear form AjXj where each Aj is a bounded linear operator in . 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
Milestones
Received: 2 April 1976
Published: 1 February 1977
Authors
Jeffrey Lynn Spielman