Some remarks on periodically correlated processes in complete correlated actions
by
Ilie Valusescu
Institute of Mathematics "Simion Stoilow", Bucharest, Romania.

For a periodically correlated process in a right L(E)-module H, an appropriate stationary process is attached such that Gladyshev's theorem is satisfied. This fact will permit us to obtain an operatorial linear filter for the prediction of the periodic process in terms of the coefficients of the maximal outer function of the attached stationary process. Also, for the prediction error, which is a periodic function in this case, an evaluation is obtained in terms of the same coefficients. To do this, some operator models are constructed and specific properties are obtained in the context of complete correlated actions.

Date received: June 13, 2008