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

被引：31
|
作者：
Shapiro, Alexander [1 ]
Xu, Huifu
机构：
[1] Georgia Inst Technol, Sch Ind & Syst Engn, Atlanta, GA 30332 USA
[2] Univ Southampton, Sch Math, Southampton SO17 1BJ, Hants, England
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2007年 / 325卷 / 02期
基金：
英国工程与自然科学研究理事会; 美国国家科学基金会;
关键词：
random sets; Artstein-Vitale law of large numbers; set-valued mappings; uniform LLN; generalized gradients; Stochastic programming; sample average approximation;
D O I：
10.1016/j.jmaa.2006.02.078
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (c) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码：1390 / 1399
页数：10
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