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Stable non-standard imprecise probabilities. (English) Zbl 1461.03022
Laurent, Anne (ed.) et al., Information processing and management of uncertainty in knowledge-based systems. 15th international conference, IPMU 2014, Montpellier, France, July 15–19, 2014. Proceedings. Part III. Cham: Springer. Commun. Comput. Inf. Sci. 444, 436-445 (2014).
Summary: Stability arises as the consistency criterion in a betting interpretation for hyperreal imprecise previsions, that is imprecise previsions (and probabilities) which may take infinitesimal values. The purpose of this work is to extend the notion of stable coherence introduced in [the second author et al., Int. J. Approx. Reasoning 54, No. 5, 573–589 (2013; Zbl 1316.03009)] to conditional hyperreal imprecise probabilities. Our investigation extends the de Finetti-Walley operational characterisation of (imprecise) prevision to conditioning on events which are considered “practically impossible“ but not “logically impossible”.
For the entire collection see [Zbl 1385.68008].

MSC:
03B48 Probability and inductive logic
03B50 Many-valued logic
28E05 Nonstandard measure theory
06D35 MV-algebras
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