Given a (finitely additive) full conditional probability space and a conditional measurable space , a multivalued mapping Γ from X to Y induces a class of full conditional probabilities on . A closed form expression for the lower and upper envelopes ⁎ and ⁎ of such class is provided: the envelopes can be expressed through a generalized Bayesian conditioning rule, relying on two linearly ordered classes of (possibly unbounded) inner and outer measures. For every , ⁎ is a normalized totally monotone capacity which is continuous from above if is a countably additive full conditional probability space and is a σ-algebra. Moreover, the full conditional prevision functional M induced by μ on the set of -continuous conditional gambles is shown to give rise through Γ to the lower and upper full conditional prevision functionals ⁎ and ⁎ on the set of -continuous conditional gambles.

Upper and lower conditional probabilities induced by a multivalued mapping / Petturiti, Davide; Vantaggi, Barbara. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 458:2(2018), pp. 1214-1235. [10.1016/j.jmaa.2017.10.006]

Upper and lower conditional probabilities induced by a multivalued mapping

Vantaggi, Barbara
2018

Abstract

Given a (finitely additive) full conditional probability space and a conditional measurable space , a multivalued mapping Γ from X to Y induces a class of full conditional probabilities on . A closed form expression for the lower and upper envelopes ⁎ and ⁎ of such class is provided: the envelopes can be expressed through a generalized Bayesian conditioning rule, relying on two linearly ordered classes of (possibly unbounded) inner and outer measures. For every , ⁎ is a normalized totally monotone capacity which is continuous from above if is a countably additive full conditional probability space and is a σ-algebra. Moreover, the full conditional prevision functional M induced by μ on the set of -continuous conditional gambles is shown to give rise through Γ to the lower and upper full conditional prevision functionals ⁎ and ⁎ on the set of -continuous conditional gambles.
2018
Finite additivity; Lower conditional prevision; Multivalued mapping; Probability envelopes; Totally monotone capacity; Analysis; Applied Mathematics
01 Pubblicazione su rivista::01a Articolo in rivista
Upper and lower conditional probabilities induced by a multivalued mapping / Petturiti, Davide; Vantaggi, Barbara. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 458:2(2018), pp. 1214-1235. [10.1016/j.jmaa.2017.10.006]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1051928
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