Duality Theory and Transfers for Stochastic Order Relations

Abstract

In this paper it will be demonstrated how functional analytic tools from duality theory can be used to give interesting characterizations of stochastic order relations for discrete distributions in terms of mass transfer principles. A general result for a large class of integral stochastic orders will be derived, and it will be shown that this applies to many important examples like usual stochastic order, convex order, supermodular order, directional convex order, and orthant orders.