Summary
In this paper the notion of coherent prevision given by de Finetti for bounded random quantities is extended to arbitrary ones. It is shown that the main properties of de Finetti’s prevision are preserved by the extended notion and some of his conjectures on previsions of unbounded random quantities are proved. Finally, a representation theorem for finite previsions in terms of Riemann-Stieltjes integral is given for random quantities defined on a common partition of the certain event and an ensuing possible interpretation for modelling real situations is discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Berti, P. andRegazzini, E. andRigo, P. (1994), Coherent prevision of random elements.C.N.R., Istituto per le applicazioni della matematica, Milano.
Bhaskara Rao, K. P. S. andBhaskara Rao, M. (1983),Theory of charges, New York: Academic Press.
Crisma, L. (1990), Un approccio alla descrizione e valutazione dei numeri aleatori. InScritti in omaggio a Luciano Daboni, Pubbl. n. 2 Dip. Mat. Appl. Sci. Econom. Statist. Attuar. «Bruno de. Finetti», Trieste: Lint.
Crisma, L. (1996), Events and Conditionals Events: a subjectivistic approach. InProceedings of the International Conference «Tbe Notion of Event in Probabilistic Epistemology», Pubbl. n. 4 Dip. Mat. Appl. Sci. Econom. Statist. Attuar. «Bruno de Finetti», Trieste: Lint.
Crisma, L. andGigante, P. andMillossovich, P. (1997), A notion of coherent prevision for arbitrary random numbers.Quad. Dip. Mat. Appl. Sci. Econom. Statist. Attuar. «Bruno de Finetti», 5/97, Univ. Trieste.
DeFinetti, B. (1938),Calcolo delle probabilità. Lecture notes, Universita di Padova (1937–38), printed inAtti del Xl Convegno AMASES, Aosta, 1987.
De Finetti, B. (1970),Teoria delle probabilità, Einaudi, Torino (English translation: B.De Finetti (1990),Theory of probability, Wiley Classics Library Edition, Chichester).
De Finetti, B. (1990),Theory of probability, Wiley Classics Library Edition, Chichester.
De Finetti, B. (1972a),Probability, induction and statistics, Wiley, New York.
De Finetti, B. (1972b), On the axiomatization of probability theory. In de Finetti (1972a), 67–113.
Dubins, L. E. (1977), On everywhere-defined integrals.Trans. Amer. Math. Soc., 232, 187–194.
Gigante, P. (1994), Previsioni di numeri aleatori limitati e loro rappresentazioni integrali.Quad. Dip. Mat. Appl. Sci. Econom. Statist. Attuar. «Bruno de Finetti», 2/94, Univ. Trieste.
Holzer, S. (1985), On coherence and conditional prevision.Boll. Un. Mat. Ital., Serie VI, Vol. IV - c, n. 1.
Regazzini, E. (1983), Sulle probabilità coerenti nel senso di de Finetti, CLUEB, Bologna.
Author information
Authors and Affiliations
Additional information
Work performed under the auspicies of the MURST gran «Statistical models: Probabilistic foundations and procedures for inference and decisions».
Rights and permissions
About this article
Cite this article
Crisma, L., Gigante, P. & Millossovich, P. A notion of coherent revision for arbitrary random quantities. J. Ital. Statist. Soc. 6, 233 (1997). https://doi.org/10.1007/BF03178914
DOI: https://doi.org/10.1007/BF03178914