Propagation of Uncertainty in a Continuous Time Dynamical System 269
with Y(t) = (Y
1
(t), Y
2
(t), . . . , Y
ν
(t))
T
is a ν-dimensional cor related stochastic
process independent of random initial vector X
0
. Moreover we allow that
Y(t) may be dependent on the states; tha t is, there exists a feedback between
the states of the s ystem (7.115) and the driving process. Our formulation is
partly motivated by applications in optimal control.
By Section 7.1.7.3 we know that (7.115) with the driving process { Y(t) :
t ≥ 0} taken as a Gaussian colored noise is often found useful in a wide range
of applications. In addition, Equation (7.1 15) with the driving process chosen
as a continuous time Markov chain has been used in engineering for investi-
gating the dynamic ...