Moderate deviation probabilities for open convex sets: nonlogarithmic behavior

Revision Rules for Convex Sets of Probabilities

Independence Concepts for Convex Sets of Probabilities

In this paper we study different concepts of independence for convex sets of probabilities. There will be two basic ideas for independ­ ence. The first is irrelevance. Two variables are independent when a change on the know­ ledge about one variable does not affect the other. The second one is factorization. Two variables are independent when the joint con­ vex set of probabilities can be decom...

Small-Ball Probabilities for the Volume of Random Convex Sets

We prove small-deviation estimates for the volume of random convex sets. The focus is on convex hulls and Minkowski sums of line segments generated by independent random points. The random models considered include (Lebesgue) absolutely continuous probability measures with bounded densities and the class of log-concave measures.

Calculating Uncertainty Intervals from Conditional Convex Sets of Probabilities

In Moral, Campos (1991) and Cano, Moral, Verdegay-L6pez (1991) a new method of con­ ditioning convex sets of probabilities has been proposed. The result of it is a convex set of non-necessarily normalized probability dis­ tributions. The normalizing factor of each probability distribution is interpreted as the possibility assigned to it by the conditioning information. From this, it is deduced ...

Log-level Comparison for Small Deviation Probabilities

Log-level comparisons of the small deviation probabilities are studied in three different but related settings: Gaussian processes under the L2 norm, multiple sums motivated by tensor product of Gaussian processes, and various integrated fractional Brownian motions under the sup-norm. ∗Department of Mathematics, University of Idaho, Moscow, ID 83844-1103, [email protected]. Research partially ...