Lower Previsions for Unbounded Random Variables

  • Matthias C. M. Troffaes
  • Gert de Cooman
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 16)


In order to generalise Walley’s theory of lower previsions, which are real-valued maps on bounded random variables, to arbitrary random variables, we introduce extended lower previsions as extended real-valued maps on arbitrary, not necessarily bounded, random variables. We suggest and motivate conditions for avoiding sure loss, coherence and linearity, we construct a natural extension, and we suggest a way to generalise some of the more advanced topological results from the existing theory of lower previsions.


Linear Space Rational Agent Natural Extension Linear Prevision Lower Prevision 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Chevé and R. Congar, Optimal pollution control under imprecise environmental risk and irreversibility, Risk Decision and Policy 5 (2000), 151–164.CrossRefGoogle Scholar
  2. 2.
    Lucio Crisma, Patrizia Gigante, and Pietro Millossovich, A notion of coherent prevision for arbitrary random quantities, Journal of the Italian Statistical Society 6 (1997), no. 3, 233–243.CrossRefGoogle Scholar
  3. 3.
    G. de Cooman, F. G. Cozman, S. Moral, and P. Walley (eds.), ISIPTA ‘89 — proceedings of the first international symposium on imprecise probabilities and their applications, Ghent, Imprecise Probabilities Project, 1999.Google Scholar
  4. 4.
    Gert de Cooman and Matthias C. M. Troffaes, Lower previsions for unbounded random variables,Tech. report, Universiteit Gent, Onderzoeksgroep SYSTeMS, 2002, In progress.Google Scholar
  5. 5.
    Matthias C. M. Troffaes and Gert de Cooman, Extension of coherent lower previsions to unbounded random variables, accepted for IPMU 2002 (The 9th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, 1–5 July 2002, Annecy, France).Google Scholar
  6. 6.
    Matthias C. M. Troffaes and Gert de Cooman, Dynamical programming for deterministic discrete-time systems with uncertain gain, Submitted, 2002.Google Scholar
  7. 7.
    Lev V. Utkin and Sergey V. Gurov, Imprecise reliability models for the general lifetime distribution classes,In De Cooman et al. [3], pp. 333–342.Google Scholar
  8. 8.
    Peter Walley, Statistical reasoning with imprecise probabilities, Chapman and Hall, London, 1991.CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Matthias C. M. Troffaes
    • 1
  • Gert de Cooman
    • 1
  1. 1.SYSTeMS Research GroupGhent UniversityZwijnaardeBelgium

Personalised recommendations