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Modeling and Inverse Problems in the Presence of Uncertainty
book

Modeling and Inverse Problems in the Presence of Uncertainty

by H. T. Banks, Shuhua Hu, W. Clayton Thompson
April 2014
Intermediate to advanced content levelIntermediate to advanced
405 pages
13h
English
Chapman and Hall/CRC
Content preview from Modeling and Inverse Problems in the Presence of Uncertainty
28 Modeling and In verse Problems in the Presence of Uncertainty
which implies that the characteristic function Π is essentially the Fourier
transform of the probability density function p of X. Hence, p can be uniquely
determined from the inverse Fourier transform of its associated characteristic
function and is given by
p(x) =
1
2π
Z
−∞
exp (iςx) Π(ς)dς. (2.70)
Interested readers are referred to some popular books such as [5, 16, 19] for
more info rmation on the Fourier transform and its applications.
The characteristic function has many useful properties. For example, Π is
bounded by Π(0) = 1, which can be dire ctly deduced from (2.69). In addition, ...
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Publisher Resources

ISBN: 9781482206432