Density Evolution Under Delayed Dynamics by Jérôme Losson & Michael C. Mackey & Richard Taylor & Marta Tyran-Kamińska
Author:Jérôme Losson & Michael C. Mackey & Richard Taylor & Marta Tyran-Kamińska
Language: eng
Format: epub
ISBN: 9781071610725
Publisher: Springer US
The moments of the measure are also given by the power series expansion of the characteristic functional as we next discuss.
5.2.3 Taylor Series Expansion of the Functional
The expression for the series expansion of a functional can be understood with the following argument. Let
be a function of k variables. The power series expansion of F is
where
Passing to a continuum in the following sense
we obtain the corresponding series expansion of a functional Ψ:
where
Ψ[y] is called the characteristic functional of the functions .
With these conventions, the expansion of the characteristic functional (5.35) is
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