After u, v are determined, @},Qo, or R,w,, can be easily derived from u, v by 
Eq. 6.90. 
b. When aj = 4ao (k?>1): 
We can set 
Ay =-utv 
6.98 
A2 =-Uu-V. 
Then computing the necessary elements for P in Eq. 6.86 in a similar way, we get 
My t+h2= iAt 4 pA2At — euAt. 2 cosh (vAr) 
fy —M2 = eo“! .2 sinh (vA) 
1 —pypz = eA’ .2 sinh (uAr) 
(6.99) 
1 + Myly = e““" 2 cosh (uAt) 
(41 +2) (Ur —f2) = 2 € #4" sinh (2vAr) 
(1 —p2u3) = 2 &*' sinh (QuAd). 
Inserting these values in Eq. 6.86 for P gives, after manipulation, 
u sinh (2vAr)—v sin (2uAr) 
= (6.100) 
2u sinh (vAt) cosh (uAt)—2v cosh (vAt) sinh (uAt) 
Then 
be u [2P sinh (vAt) cosh (uAt)— sinh (2vAr)] (6.101) 
2P cosh (vAt) sinh (uAt)— sinh (2uAr) 
As were for at < 4a, the sin, cos, sinh, cosh functions are expressed by a, a for 
this case. Therefore, after v and u have been determined, @1,@2 or K, w,, can be deter- 
mined from u, v easily. Their derivations are omitted here because we are usually less 
concerned with the case when k*>1. 
For this case, the coefficients @),Q@o or K, w, of the differential equation are 
derived from a, a2, and b; uniquely. The differential equation which expresses the con- 
tinuous autoregressive process can be obtained from the parameters a), a2, and b, of the 
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