FUSIONS OF A PROBABILITY-DISTRIBUTION
成果类型：
Article
署名作者：
ELTON, J; HILL, TP
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989936
发表日期：
1992
页码：
421-454
关键词：
摘要：
Starting with a Borel probability measure P on X (where X is a separable Banach space or a compact metrizable convex subset of a locally convex topological vector space), the class F(P), called the fusions of P, consists of all Borel probability measures on X which can be obtained from P by fusing parts of the mass of P, that is, by collapsing parts of the mass of P to their respective barycenters. The class F(P) is shown to be convex, and the ordering induced on the space of all Borel probability measures by Q curly less than or equal to P if and only if Q is-an-element-of F(P) is shown to be transitive and to imply the convex domination ordering. If P has a finite mean, then F(P) is uniformly integrable and Q curly less than or equal to P is equivalent to Q convexly dominated by P and hence equivalent to the pair (Q, P) being martingalizable. These ideas are applied to obtain new martingale inequalities and a solution to a cost-reward problem concerning optimal fusions of a finite-dimensional distribution.