Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900285 | Journal of Mathematical Analysis and Applications | 2018 | 30 Pages |
Abstract
Given a (finitely additive) full conditional probability space (X,FÃF0,μ) and a conditional measurable space (Y,GÃG0), a multivalued mapping Î from X to Y induces a class of full conditional probabilities on (Y,GÃG0). A closed form expression for the lower and upper envelopes μâ and μâ 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 BâG0, μâ(â
|B) is a normalized totally monotone capacity which is continuous from above if (X,FÃF0,μ) is a countably additive full conditional probability space and F is a Ï-algebra. Moreover, the full conditional prevision functional M induced by μ on the set of F-continuous conditional gambles is shown to give rise through Î to the lower and upper full conditional prevision functionals Mâ and Mâ on the set of G-continuous conditional gambles. For every BâG0, Mâ(â
|B) is a totally monotone functional having a Choquet integral expression involving μâ. Finally, by considering another conditional measurable space (Z,HÃH0) and a multivalued mapping from Y to Z, it is shown that the conditional measures μââ, μââ and functionals Mââ, Mââ induced by μâ preserve the same properties of μâ,μâ and Mâ, Mâ.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Davide Petturiti, Barbara Vantaggi,