The second term vanishes since dw(t) and es) are independent if 
ESL hel Sieyeicenicis 
cae Rs) = [A(e) — Ke ©) (ey) Elx(e) x'(s)] H'(s) 
ie 
es | a Ge r) H(r) E[x(r) (Ss) I H! (s) dr 
0 t 
Use of the integral equation (5.8) to obtain an expression for 
E[x(t) x e)j H (s) yields 
[2K 2) + eee, 0) HCE) KOE, 8) — ACE) KEE, 99] RYO 
ie 
ai [28g + K(t, t) H(t) K(t, r) - A(t) K(t, o| 
0 
H(x) Elx(r) x (s)] H’(s) dr (5.9) 
Set 
Die, s) = {EE 8) 4 Kee, ty H(t) K(t, s) - A(t) K(t, 5) 
Then by (5.9) 
t 
Y(t, s) = - I Ue, x) Wr) Elx(e) x"(s)] W'(s) RUv(s) dr 
0 
(5.10) 
Since the kernel of this integral equation corresponds to a positive 
definite quadratic form, the only solution of (5.10) is 
UGS) =O 
58 
