On a uniform law of large numbers for random sets and subdifferentials of random functions

Pedro Terán

Statistics & Probability Letters, 2008, vol. 78, issue 1, 42-49

Abstract: In this paper, we strengthen the convergence in a uniform law of large numbers for random upper semicontinuous multifunctions of Shapiro and Xu. The proof is based on an abstract law of large numbers in a metric space endowed with a convex combination operation. Convergence in the Hausdorff metric is obtained, whereas the original result presented a weakened form of convergence of excess functionals. As a consequence, another law of large numbers for subdifferentials of random functions is improved as well.

Keywords: Clarke; generalized; gradient; Uniform; strong; law; of; large; numbers; Upper; semicontinuous; multifunction; Subdifferential (search for similar items in EconPapers)
Date: 2008
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