On the Necessary and Sufficient Conditions for Peng's Law of Large Numbers Under Sublinear Expectations  

作　　者：Xinpeng LI Gaofeng ZONG 

机构地区：[1]Research Center for Mathematics and Interdisciplinary Sciences,Frontiers Science Center for Nonlinear Expectations(Ministry of Education),Shandong University,Qingdao 266237,Shandong,China [2]School of Statistics and Mathematics,Shandong University of Finance and Economics,Jinan 250014,China

出　　处：《Chinese Annals of Mathematics,Series B》2025年第1期139-150,共12页数学年刊(B辑英文版)

基　　金：supported by the National Natural Science Foundation of China(Nos.12326603,11601281,11501325);the National Key R&D Program of China(No.2018YFA0703900);the Natural Science Foundation of Shandong Province(No.ZR2021MA018);the Social Science Planning Project of Shandong Province(No.24CJJJ18);the Qilu Scholars Program of Shandong University。

摘　　要：In this paper,the authors firstly establish the weak laws of large numbers on the canonical space(R^(N),B(R^(N)))by traditional truncation method and Chebyshev’s inequality as in the classical probability theory.Then they extend them from the canonical space to the general sublinear expectation space.The necessary and sufficient conditions for Peng’s law of large numbers are obtained.

关 键 词：Canonical space Independence and identical distribution Peng's law of large numbers Sublinear expectation 

分 类 号：O17[理学—数学]