
Propagation of Uncertainty in a Continuous Time Dynamical System 239
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−100
−80
−60
−40
−20
0
20
40
60
80
100
t
Gaussian white noise
FIGURE 7.3: A realization of Ga ussian white noise with D = 1/2 on the
time interval [0, 1].
The prope rties of normal a nd independent increments of the Wiener pro-
cess imply that GWN
j
, j = 0, 1, 2, . . . , 1000, are independent and normally
distributed with mean zero and variance
1
t
j
− t
j−1
= 1000. Fig ure 7.3 in-
dicates that Gaussian white noise is extremely irregular and is nowhere
continuous.
7.1.7.2.2 White shot noise White shot noise is another white noise that
has been extensively studied ...