The purpose of this paper is to show that many integral stochastic orders have a generator consisting of infinitely differentiable functions. This especially holds for all stochastic orders with characterizations via difference operators. The usefulness of this result is demonstrated in two applications relating to stochastic ordering of multivariate normal distributions and ordering of random vectors in a random environment.
"Smooth generators of integral stochastic orders." Ann. Appl. Probab. 12 (4) 1174 - 1184, November 2002. https://doi.org/10.1214/aoap/1037125858