Remarks on stochastic model reduction

In this note, we give a solution to the stochastic system model reduction problem in terms of the approximation of the output stochaslic process power spectrum by applying balanced realization or optimal Hankel norm approximation to the asymptotically stable and minimum phase spectral factor. We also give explicit bounds for the approximation error. The effectiveness of this method is compared to the one by Jonckheere and Helton.