Integral Representation of Coherent Lower Previsions by Super-Additive Integrals
نویسندگان
چکیده
منابع مشابه
Continuous Linear Representation of Coherent Lower Previsions
This paper studies the possibility of representing lower previsions by continuous linear functionals. We prove the existence of a linear isomorphism between the linear space spanned by the coherent lower previsions and that of an appropriate space of continuous linear functionals. Moreover, we show that a lower prevision is coherent if and only if its transform is monotone. We also discuss the ...
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Walley’s theory of coherent lower previsions builds upon the former theory by Williams with the explicit aim to make it deal with conglomerability. We show that such a construction has been only partly successful because Walley’s founding axiom of joint coherence does not entirely capture the implications of conglomerability. As a way to fully achieve Walley’s original aim, we propose then the ...
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We study n-monotone lower previsions, which constitute a generalisation of n-monotone lower probabilities. We investigate their relation with the concepts of coherence and natural extension in the behavioural theory of imprecise probabilities, and improve along the way upon a number of results from the literature. Finally, we indicate how many approaches to integration in the literature fall sq...
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This is an introduction to the concepts of lower and upper prevision and the mathematical theory of coherence. Upper and lower previsions are generalisations of upper and lower probabilities. They can model a very wide variety of kinds of uncertainty, partial information and ignorance. The theory of coherent lower previsions is based on a simple behavioural interpretation of lower previsions. T...
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We study the conformity of marginal unconditional and conditional models with a joint model under assumptions of epistemic irrelevance and independence, within Walley’s theory of coherent lower previsions. By doing so, we make a link with a number of prominent models within this theory: the marginal extension, the irrelevant natural extension, the independent natural extension and the strong pr...
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ژورنال
عنوان ژورنال: Axioms
سال: 2020
ISSN: 2075-1680
DOI: 10.3390/axioms9020043