Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Chevé and R. Congar, Optimal pollution control under imprecise environmental risk and irreversibility, Risk Decision and Policy 5 (2000), 151–164.
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.
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.
Gert de Cooman and Matthias C. M. Troffaes, Lower previsions for unbounded random variables,Tech. report, Universiteit Gent, Onderzoeksgroep SYSTeMS, 2002, In progress.
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).
Matthias C. M. Troffaes and Gert de Cooman, Dynamical programming for deterministic discrete-time systems with uncertain gain, Submitted, 2002.
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.
Peter Walley, Statistical reasoning with imprecise probabilities, Chapman and Hall, London, 1991.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Troffaes, M.C.M., de Cooman, G. (2002). Lower Previsions for Unbounded Random Variables. In: Grzegorzewski, P., Hryniewicz, O., Gil, M.Á. (eds) Soft Methods in Probability, Statistics and Data Analysis. Advances in Intelligent and Soft Computing, vol 16. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1773-7_13
Download citation
DOI: https://doi.org/10.1007/978-3-7908-1773-7_13
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-1526-9
Online ISBN: 978-3-7908-1773-7
eBook Packages: Springer Book Archive