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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
A Stochastic System and Its Corresponding Deterministic System 329
Define g(c) =
l
X
j=1
v
j
f
j
(c). Then by (8.32), Lemma 8.3.1 and Gronwall’s in-
equality, one can s how that with some mild co nditio ns on g the processes
{C
M
(t) : t 0} converge to a deterministic process that is the solution of the
following system of o rdinary differential equations :
˙
c(t) = g(c), c(0) = c
0
. (8.33)
This result was originally shown by Kurtz [34, 35] (and hence it is referred
to as Kurtz’s limit t heorem in this monograph), and is summarized in the
following theorem (e.g., see [9, 36] for details on the proof).
Theorem 8.3.3 Suppose that lim
M→∞
C
M
(0) = c
0
and for any compact set
R
n
there exists a positive constant η
such that
|g(c) g(
˜
c)| η
|c
˜
c|, c,
˜
c .
Then we ...
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Publisher Resources

ISBN: 9781482206432