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On minimal splitting subspaces and markovian representations

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Abstract

Given a Hilbert spaceH, letH 1 andH 2 be two arbitrary subspaces. The problem of finding all minimal splitting subspaces ofH with respect toH 1 andH 2 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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Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, 40506, Lexington, Kentucky, USA

    Anders Lindquist

  2. Laboratorio per Ricerche di Dinamica dei Sistemi e di Elettronica Biomedica, Consiglio Nazionale delle Ricerche, 35100, Padova, Italy

    Giorgio Picci

  3. Centre de Mathematiques Appliquées, Ecole Polytechnique, 91128, Palaiseau Cedex, France

    Guy Ruckebusch

Authors
  1. Anders Lindquist
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  2. Giorgio Picci
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  3. Guy Ruckebusch
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Additional information

Research sponsored by the Air Force Office of Scientific Research under Grant No. AFOSR-78-3519.

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Lindquist, A., Picci, G. & Ruckebusch, G. On minimal splitting subspaces and markovian representations. Math. Systems Theory 12, 271–279 (1978). https://doi.org/10.1007/BF01776578

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