Large Deviations of Random Sets and Random Upper Semicontinuous Functions

摘要

In this paper, we obtain large deviations (necessary and sufficient conditions) of random sets which take values of bounded closed convex sets on the underling separable Banach space with respect to the Hausdorff distance dH. We also give necessary and sufficient conditions of large deviations for random upper semicontinuous functions whose values are of bounded closed convex levels on the underling separable Banach space in the sense of the uniform Hausdorff distance d_u~∞. The main tool is the work of Wu on the large deviations for empirical processes [16].