ON APPROXIMATE STOCHASTIC-REALIZATION

The problem considered here is to represent a stationary stochastic process y with a low-dimensional stochastic model. This problem occurs when the state space of an exact realization of y has a very large dimension. The reduction is obtained in this large state space, exploiting its markovian structure to characterize all markovian subspaces, among which a reduced k-dimensional model is sought. The concept of markovian basis is introduced, and its equivalence with the Malmquist basis in the spectral domain is shown. An algorithm with polynomial complexity to compute an approximate model is given.