We establish preservation results for the stochastic comparison of multivariate random sums of stationary, not necessarily independent, sequences of nonnegative random variables. We consider convex-type orderings, i.e. convex, coordinatewise convex, upper orthant convex and directionally convex orderings. Our theorems generalize the well-known results for the stochastic ordering of random sums of independent random variables.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am30-4-2,
author = {Rafa\l\ Kulik},
title = {Stochastic comparison of multivariate random sums},
journal = {Applicationes Mathematicae},
volume = {30},
year = {2003},
pages = {379-387},
zbl = {1061.60012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am30-4-2}
}
Rafał Kulik. Stochastic comparison of multivariate random sums. Applicationes Mathematicae, Tome 30 (2003) pp. 379-387. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am30-4-2/