Abstract
Given a Hilbert spaceH, letH1 andH2 be two arbitrary subspaces. The problem of finding all minimal splitting subspaces ofH with respect toH1 andH2 is solved. This result is applied to the stochastic realization problem. Each minimal stochastic realization of a given vector processy defines a family of state spaces. It is shown that these families are precisely those families of minimal splitting subspaces (with respect to the past and the future ofy) which satisfy a certain growth condition.
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