On the solution of Stein's equation and Fisher's information matrix of an ARMAX process (Q1763819)

The authors deal with the Stein equation \(S=BSA^{\top}=\Gamma\) (\(A\in \mathbb{C}^{m\times m}\), \(B\in \mathbb{C}^{n\times n}\), \(\Gamma\in \mathbb{C}^{n\times m})\). Under some conditions on the spectra of \(A\) and \(B\) they express the solution of a Stein equation in terms of the Fisher information matrix of a scalar ARMAX process.