Characterizations of Gaussian Random Processes by Representations in Terms of Independent Random Variables.

Percy A. Pierre

ResearchPublished 1969

An investigation of certain classes of random processes having the same covariance function and some linear representations of those processes. This study considers various Gaussian and non-Gaussian models of random noise and shows that some of the most useful properties of the Gaussian model are not shared by physically reasonable non-Gaussian models. It is possible to define certain non-Gaussian processes as sums of a random number of random pulses. Necessary and sufficient conditions for the independence of linear functionals of these processes are obtained. 47 pp. (KB

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Pierre, Percy A., Characterizations of Gaussian Random Processes by Representations in Terms of Independent Random Variables. Santa Monica, CA: RAND Corporation, 1969. https://www.rand.org/pubs/research_memoranda/RM6092.html.
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