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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
284 Modeling and Inverse Problems in the Presence of Uncertainty
being some positive constants. In addition, α, γ a nd ̺ = (̺
0
, ̺
1
, . . . , ̺
m1
)
T
are non-random functions of t, and Z ·̺(t) denotes the dot product of Z and
̺(t) (that is, Z ·̺(t) = Z
T
̺(t) =
m1
X
j=0
Z
j
̺
j
(t)). The corresp onding stochastic
differential equation takes the for m
dX(t) = [α(t)X(t) + ξ(t)]dt + η(t)dW (t), X(0) = X
0
, (7.140)
where ξ and η are some non-random functions of t, and {W (t) : t 0} is a
Wiener process.
The conditions for the pointwise equivalence between the RDE (7.139) and
the SDE (7.140) are stated in the following theorem.
Theorem 7.4.6 If functions ξ, η and γ,
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Publisher Resources

ISBN: 9781482206432