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Analysis and Optimization of Systems pp 436–444Cite as

The weak stochastic realization problem for discrete-time counting processes

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 62))

Abstract

The weak stochastic realization problem is considered for discrete-time stationary counting processes. Such processes take values in the countable infinite set N={0,1,2,...}. A stochastic realization is sought in the class of stochastic systems specified by a conditional distribution for the output given the state of Poisson type, and by a finite valued state process. In the paper a necessary and sufficient condition is derived for the existence of a stochastic realization in the above specified class.

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References

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Authors and Affiliations

  1. Centre for Mathematics and Computer Science, P.O. Box 4079, 1009 AB, Amsterdam, The Netherlands

    J. H. van Schuppen

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  1. J. H. van Schuppen
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A. Bensoussan J. L. Lions

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© 1984 Springer-Verlag

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van Schuppen, J.H. (1984). The weak stochastic realization problem for discrete-time counting processes. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 62. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0004972

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  • DOI: https://doi.org/10.1007/BFb0004972

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13551-7

  • Online ISBN: 978-3-540-39007-7

  • eBook Packages: Springer Book Archive

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