ie iG 
a i | Kes HG) ss) dv (s) dr 
0 
uF { Kes) idviGs) x! (s) H. (s) ds 
0 Oo 
t TE 
+ | | K(t, r) dv(r) ee) 
0 fe) 
From the properties of Wiener processes, 
i iG E 
E { | K(t, r) dv(r) aa (a) = i K(t, s) R (s) ds 
oO we Oo Mi 
where R is the covariance matrix of the process. Furthermore, 
dv(s) and x(s) are independent, so E dv(r) ae) = 0; hence 
ie 
as 
Elx(t) (2(t) - 2(0))"] = | | | K(t, x) H(r) Elx(e) x (s)] 
fo) 0 
(5.7) 
Et (e) dr + K(t, s) ol ds 
for all o and t. On the other hand, from (5.3) 
E T 
Bint) @@) = B@))"] =m Ee { ils) «(e) ds + vio | 
0 
T 
| BinGe) <a) ECs) ae 
oO 
i is 
= i i K(t, r) H(r) Elx(r) x'(s)] H'(s) dr 
0 
oO 
+ K(t, s) RCs) ds 
56 
