We can then write a generalized covariance function (assumed to 

 be finite) as the matrix equation 



R(T) = E.[N''(t) N(t*T)J 



■r(o,o,t) R(X,YJ)' 

 R(-X,--Y,T^ Rro,0,TM (4.2) 



Now R(-T) is 



R(-T) = 



rR(^,o,-T) R(x,Y. -T) 



jl(-XrY-T) R(o,o,-T)_ 



and R(-T) transpose is 



R(-T) 



(4.3) 



R(X,Y,-T) R^o, o, -T^_^ 



We have by Equation (3.3) and stationarity that 



R(-X,-Y;-T) =■ LC'lCx.^y^t-^T) 7(^-»2t->-t)) 



= E(7r<..^-.t\ '^/x^.if^ttT)) = R (X,Y,T) ^^ ^^ 



It then follows that 



R(T) = H(-T) 



(4.5) 



13 



