ON LINEAR PREDIKTORS FOR NON –STATTIONARY PROCESSES

ALEKSANDER KOWALSKI [1] has shown, among other things,that there exists a unique, bounded solution of (1) and that the prediction formulas used for invertible stationary ARMA models are valid also for (1)-(2).
Let denote the probability spase with the filtration( non-increasing sequence of sub- -fields of the -field ). The -field is interpreted as the -field of all events prior to and including time let denote a Hilbert space of zero mean random variables defined on with finite second moments. Define on the adapted process where is measurable for every such that