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Ergodicity Conditions for Upper Transition Operators

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Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods (IPMU 2010)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 80))

Abstract

We study ergodicity for upper transition operators: bounded, sub-additive and non-negatively homogeneous transformations of finite-dimensional linear spaces. Ergodicity provides a necessary and sufficient condition for Perron–Frobenius-like convergence behaviour for upper transition operators. It can also be characterised alternatively using accessibility relations: ergodicity is equivalent with there being a single maximal communication (or top) class that is moreover regular and absorbing. We present efficient algorithms for checking these conditions.

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Author information

Authors and Affiliations

  1. SYSTeMS Research Group, Ghent University, Technologiepark–Zwijnaarde 914, 9052, Zwijnaarde, Belgium

    Filip Hermans & Gert de Cooman

Authors
  1. Filip Hermans
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  2. Gert de Cooman
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Editor information

Editors and Affiliations

  1. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Marburg, Germany

    Eyke Hüllermeier

  2. Department of Knowledge Processing and Language Engineering, Otto-von-Guericke University of Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Rudolf Kruse

  3. Fakultät für Elektrotechnik und Informationstechnik, Technische Universität Dortmund, 44221, Dortmund, Germany

    Frank Hoffmann

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Hermans, F., de Cooman, G. (2010). Ergodicity Conditions for Upper Transition Operators. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods. IPMU 2010. Communications in Computer and Information Science, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14055-6_8

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  • DOI: https://doi.org/10.1007/978-3-642-14055-6_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14054-9

  • Online ISBN: 978-3-642-14055-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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