dx(t) - dx(t) 
a 
bald 
i 
=i] ES 
Axdt+dw-Adt-PHR (dv + H(t) x) 
at till 
Ni de 4 dw — PH Ras dv - PH RL H x dt 
[A= pe a a] & des@n ep ae ee ae 
with x(0) = x(0). By the methods developed in the previous section 
for stochastic differential equations, 
P(t) = E[x(t) x2 (t)] 
ie 
a(t, 0) To (t, 0) + { (t, 0) [Q(o) 
0 
+ 
P(o) HE (0) R-* (0) HG) Bo] OE. o) de Gil) 
where ®(t, T) is the transport matrix associated with the linear 
differential equation 
dy a a i il! 
ae (A - PH RL H) y Ges) 
and where 
Q dc = Bide) Gy Gy (5.16) 
from (4.11) 
dP i 1 T 
SS = Pek ae H) P + P(A - P He Ro H) 
£ Oe) put Se H Pl 
61 
