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Realizations of reciprocal processes

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Modelling and Adaptive Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 105))

Abstract

We review the concept of a reciprocal process and show that a stationary Gaussian reciprocal process, which satisfies a certain technical assumption, can be realized by a linear stochastic differential equation with independent initial condition.

Research supported in part by NSF under DMS-8601635.

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References

  1. Bernstein, S., Sur les laisons entre les grandeurs aleatoires, Proc. of Int. Cong. of Math., Zurich (1932) 288–309.

    Google Scholar 

  2. Mehr, C. B. and McFadden, J. A., Certain properties of Gaussian processes and their first passage times, J. Roy. Stat. Soc. B27 (1965) 505–522.

    Google Scholar 

  3. Jamison, D., Reciprocal processes: the stationary Gaussian case, Ann. Math. Stat. 41 (1970) 1624–1630.

    Google Scholar 

  4. Chay, S. C., On quasi-Markov random fields, J. Multivar. Anal. 2 (1972) 14–76.

    Google Scholar 

  5. Carmichael, J-P., Masse, T-C. and Theodorescu, R., Processus gaussiens stationaires reciproques sur un intervalle, C. R. Acad. Sc. Paris, Serie I 295 (1982) 291–293.

    Google Scholar 

  6. Doob, J. L., Stochastic Processes (Wiley, N.Y. 1953).

    Google Scholar 

  7. Krener, A. J., Reciprocal Processes and the Stochastic Realization Problem for Acausal Systems, in Modeling, Identification and Robust Control, C. I. Byrnes and A. Lindquist, eds., North-Holland, Amsterdam, 1986, 197–211.

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Authors and Affiliations

  1. Department of Mathematics and the Institute of Theoretical Dynamics, University of California, 95616, Davis, CA, USA

    Arthur J. Krener

Authors
  1. Arthur J. Krener
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Editor information

Christopher Ian Byrnes Alexander B. Kurzhanski

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© 1988 Springer-Verlag

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Krener, A.J. (1988). Realizations of reciprocal processes. In: Byrnes, C.I., Kurzhanski, A.B. (eds) Modelling and Adaptive Control. Lecture Notes in Control and Information Sciences, vol 105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043182

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  • DOI: https://doi.org/10.1007/BFb0043182

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19019-6

  • Online ISBN: 978-3-540-38904-0

  • eBook Packages: Springer Book Archive

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