Probabilistic, Statistical, and Other Applications

Abstract

In this chapter are collected a variety of probabilistic results closely related to those of Chapter 11, but which differ in various ways. The relationships of Chapter 11 between pairs of random vectors all reduce to ordinary majorization when the random vectors are de- generate. There are additional conditions for random vectors which do not have this qualification to be called “stochastic majorizations” but which can still be put into the general form PC : f(X) =st f(Y) for all f C, or 8 EC : Ef(X) = Ef(Y ) for all f C such that the expectations are defined.