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Stochastic realization problems

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Three Decades of Mathematical System Theory

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 135))

Abstract

The stochastic realization problem asks for the existence and the classification of all stochastic systems for which the output process equals a given process in distribution or almost surely. This is a fundamental problem of system and control theory. The stochastic realization problem is of importance to modelling by stochastic systems in engineering, biology, economics etc. Several stochastic systems are mentioned for which the solution of the stochastic realization problem may be useful. As an example recent research on the stochastic realization problem for the Gaussian factor model and a Gaussian factor system is discussed.

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Authors and Affiliations

  1. Centre for Mathematics and Computer Science (CWI), Kruislaan 413, 1098 SJ, Amsterdam, the Netherlands

    J. H. van Schuppen

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  1. J. H. van Schuppen
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Hendrik Nijmeijer Johannes M. Schumacher

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This paper is dedicated to J. C. Willems on the occasion of his fiftieth birthday.

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van Schuppen, J.H. (1989). Stochastic realization problems. In: Nijmeijer, H., Schumacher, J.M. (eds) Three Decades of Mathematical System Theory. Lecture Notes in Control and Information Sciences, vol 135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0008474

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  • DOI: https://doi.org/10.1007/BFb0008474

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