A NOTE ON THE INTERVAL-VALUED MARGINAL PROBLEM AND ITS MAXIMUM-ENTROPY SOLUTION

This contribution introduces the marginal problem, where marginals are not given precisely, but belong to some convex sets given by systems of intervals. Conditions, under which the maximum entropy solution of this problem can be obtained via classical methods using maximum entro py representatives of these convex sets, are presented. Two counterexa mples illustrate the fact, that this property is not generally satisfi ed. Some ideas of an alternative approach are presented at the end of the paper.