An Extension Problem for Discrete-Time Almost Periodically Correlated Stochastic Processes
In (D. Alpay, A. Chevreuil, Ph. Loubaton, J. Time Ser. Anal., 2000, to appear) an extension problem for covariance matrix of discrete-time periodically correlated stochastic processes introduced by Gladyshev was treated. In this paper we study the same problem for discrete-time almost periodically correlated stochastic processes. This problem can be reformulated and solved within the framework of interpolation for upper triangular operators. More precisely one can reduce the problem to an interpolation problem in the class of upper triangular operators of the Schur class.
D. Alpay, B. Freydin and Ph. Loubaton. An extension problem for discrete-time almost periodically correlated stochastic processes. Linear Algebra and its applications (308) 1-3 (2000) pp. 163-181.