Inequalities for stochastic models via supermodular orderings

The aim of this paper is to derive inequalities for random vectors by using the supermodular ordering. The properties of this ordering suggest to use it as a comparison for the “ strength of dependence” in random vectors. In contrast to already established orderings of this type, the supermodular ordering has the advantage that it is not necessary to assume a common marginal distribution for the random vectors under comparison. As a consequence we obtain new inequalities by applying it to multivariate normal distributions, Markov chains and some stochastic models

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