Strong previsions of random elements |
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Authors: | Patrizia Berti Eugenio Regazzini Pietro Rigo |
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Affiliation: | (1) Dipartimento di Matematica Pura ed Applicata “G. Vitali”, Università di Modena, Via Campi 213/B, 41100 Modena, Italy;(2) Dipartimento di Matematica “F. Casorati”, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy;(3) Dipartimento di Economia Politica e Metodi Quantitativi, Università di Pavia, Via S. Felice 5, 27100 Pavia, Italy |
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Abstract: | LetC be a class of arbitrary real random elements andP an extended real valued function onC. Two definitions of coherence forP are compared. Both definitions reduce to the classical de Finetti's one whenC includes bounded random elements only. One of the two definitions (called strong coherence) is investigated, and some criteria for checking it are provided. Moreover, conditions are given for the integral representation of a coherentP, possibly with respect to a δ-additive probability. Finally, the two definitions and the integral representation theorems are extended to the case whereC is a class of random elements taking values in a given Banach space. |
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Keywords: | Banach space coherence finite additivity integral representation strong coherence |
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