On conditional stochastic ordering of distributions

Conditional stochastic ordering is concerned with the stochastic ordering of a pair of probability measures conditional on certain subsets or sub-. -algebras. Some basic results of conditional stochastic ordering were proved by Whitt. We extend some of Whitt's results and prove a basic relation between stochastic ordering conditional on subsets and stochastic ordering conditional on . -algebras. In the second part of the paper we consider the ordering of conditional expectations. There are several different formulations of this problem motivated by different types of applications.