For all A and F(z), the criterion (5.5) requires 
me! Ge) = Syl = at = GG 2S S60 
This can be true only if 
o2nol 2. Ge =D eM aee@ = on 
But this implies that 
me @@) =a "jy <0 
for any linear combination F(z) of elements of z; hence 
ll 
E[x F (z)] = 0 (5.6) 
An integral equation for the kernel K(t, T) can be derived from 
(5.6). This kernel is not a stochastic quantity, and it can be de- 
termined independent of the realization z(*). For F(z) = z(t) - 
ZO) Ee ONO sete ee expressions (5)16)) sy lelds 
Tin) @@) =2@1 = nee) G@) = 2) 71 
e T 
E | X(t) || H(s) x(s) ds +d vo} 
O 
fe TG T 
i Ke, 7) 120 | {J H(s) x(s) ds + wo 
ll 
ea) 
———_ 
0) Oo 
t T 
te 40 
=6 | | Cy GGG ae deci (H(G)) <(G)de cera())in 
0 
2 | ee, 1) HG) ee) = Gy EE@) ds oe 
0 % 
55 
