History
Volterra series is a modernized version of the theory of analytic functionals due to the Italian mathematician Vito Volterra in work dating from 1887. Norbert Wiener became interested in this theory in the 1920's from contact with Volterra's student Paul Lévy. He applied his theory of the Brownian motion to the integration of Volterra analytic functionals. The use of Volterra series for system analysis originated from a restricted 1942 wartime report of Wiener, then professor of mathematics at MIT. It used the series to make an approximate analysis of the effect of radar noise in a nonlinear receiver circuit. The report became public after the war. As a general method of analysis of nonlinear systems, Volterra series came into use after about 1957 as the result of a series of reports, at first privately circulated, from MIT and elsewhere. The name Volterra series came into use a few years later.
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