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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
Propagation of Uncertainty in a Continuous Time Dynamical System 249
By the above equation and (7 .62) we see that the Orn stein–Uhlenbeck process
has the same form of correlation function as dichotomous Markov noise. It
should be noted that the Ornstein–Uhlenbeck process is the only process that
is simultaneou sly Gaussian, Markovian and st ationary (e.g., see [72, p. 172]
or [95, Section 2.5]—this follows from a result due to Doob), and it is often
referred to as the Markov Gaussian colored noise.
7.2.1.1 Evolution of the Probability Density Function of X (t)
Theorem 7.2.2 Assume that X
0
has probability density function p
0
, and
X(t) satisfies (7.63) ...
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Publisher Resources

ISBN: 9781482206432