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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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.
|Subjects:||Q Science > QA Mathematics|
|Divisions:||University Structure - Pre August 2011 > School of Mathematics > Operational Research
|Date Deposited:||17 Mar 2010|
|Last Modified:||02 Mar 2012 11:52|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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