Uniform laws of large numbers for set-valued mappings and subdifferentials of random functions


Shapiro, Alexander and Xu, Huifu (2007) Uniform laws of large numbers for set-valued mappings and subdifferentials of random functions. Journal of Mathematical Analysis and Applications, 325, 1390-1399. (doi:10.1016/j.jmaa.2006.02.078).

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Description/Abstract

We derive a uniform (strong) Law of Large Numbers (LLN) for random set-valued mappings. The result can be viewed as an extension of both, a uniform LLN for random functions and LLN for random sets. We apply the established results to a consistency analysis of stationary points of sample average approximations of nonsmooth stochastic programs.

Item Type: Article
ISSNs: 0022-247X (print)
Related URLs:
Subjects: Q Science > QA Mathematics
Divisions: University Structure - Pre August 2011 > School of Mathematics > Operational Research
ePrint ID: 79544
Date Deposited: 17 Mar 2010
Last Modified: 27 Mar 2014 19:01
URI: http://eprints.soton.ac.uk/id/eprint/79544

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