Skip to Main Content
Probabilistic Models for Dynamical Systems, 2nd Edition
book

Probabilistic Models for Dynamical Systems, 2nd Edition

by Haym Benaroya, Seon Mi Han, Mark Nagurka
May 2013
Intermediate to advanced content levelIntermediate to advanced
764 pages
6h 43m
English
CRC Press
Content preview from Probabilistic Models for Dynamical Systems, 2nd Edition
9.5. Determine the probability density function f
˙
R
( ˙r) of the time derivative of the envelope process for
a narrow-band Gaussian process with zero mean.
Solution: From Section 9.2.4, it is found that
f
R
˙
R
(r, ˙r) =
r
2πσ
2
X
*
σ
2
˙
X
ω
2
m
σ
2
X
exp
1
2
1
r
2
σ
2
X
+
˙r
2
σ
2
˙
X
ω
2
m
σ
2
X
2
r 0, −∞ < ˙r <
The marginal density can be obtained by
f
˙
R
( ˙r) =
0
f
R
˙
R
(r, ˙r) dr
=
1
2π
*
σ
2
˙
X
ω
2
m
σ
2
X
exp
1
2
˙r
2
σ
2
˙
X
ω
2
m
σ
2
X
for −∞ < ˙r < ,
which is a Gaussian process.
261
9.6. Find the average clump size of a narrow-band Gaussian process X (t) with one-sided spectral density
given by
S
o
(
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Adaptive Learning Methods for Nonlinear System Modeling

Adaptive Learning Methods for Nonlinear System Modeling

Danilo Comminiello, Jose C. Principe
Mathematical Methods in Dynamical Systems

Mathematical Methods in Dynamical Systems

S. Chakraverty, Subrat Kumar Jena

Publisher Resources

ISBN: 9781439849897