The Dp-metric space of set-valued random variables and its application to covariances

In this paper, we introduce the D-p-metric of set-valued random variables. We prove that the Dp-metric space of set-valued random variables is complete, and represent the equivalent propositions of convergence for set-valued random variables with respect to D-p-metric. Finally, we give several definitions of the variance, covariance and correlation coefficient of set-valued random variables by the D-p-metric, and discuss some useful results.