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Stochastic realization of a Gaussian stochastic control system

Stochastic realization of a Gaussian stochastic control system The stochastic realization problem is considered of representing a stationary Gaussian process as the observation process of a Gaussian stochastic control system. The problem formulation includes that the lastm components of the observation process form the Gaussian white noise input process to the system. Identifiability of this class of systems motivates the problem. The results include a necessary and sufficient condition for the existence of a stochastic realization. A subclass of Gaussian stochastic control systems is defined that is almost a canonical form for this stochastic realization problem. For a structured Gaussian stochastic control system an equivalent condition for identifiability of the parametrization is stated. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Stochastic realization of a Gaussian stochastic control system

Acta Applicandae Mathematicae , Volume 35 (2) – Dec 31, 2004

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References (23)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00994918
Publisher site
See Article on Publisher Site

Abstract

The stochastic realization problem is considered of representing a stationary Gaussian process as the observation process of a Gaussian stochastic control system. The problem formulation includes that the lastm components of the observation process form the Gaussian white noise input process to the system. Identifiability of this class of systems motivates the problem. The results include a necessary and sufficient condition for the existence of a stochastic realization. A subclass of Gaussian stochastic control systems is defined that is almost a canonical form for this stochastic realization problem. For a structured Gaussian stochastic control system an equivalent condition for identifiability of the parametrization is stated.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Dec 31, 2004

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