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| On the Necessary and Sufficient Conditions for Peng’s Law of Large Numbers Under Sublinear Expectations |
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Citation： |
Xinpeng LI,Gaofeng ZONG.On the Necessary and Sufficient Conditions for Peng’s Law of Large Numbers Under Sublinear Expectations[J].Chinese Annals of Mathematics B,2025,46(1):139~150 |
| Page view： 200
Net amount： 141 |
Authors： |
Xinpeng LI; Gaofeng ZONG |
Foundation： |
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) and the Qilu Scholars Program of Shandong University. |
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| Abstract： |
In this paper, the authors firstly establish the weak laws of large numbers on the
canonical space (RN, B(RN)) 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. |
Keywords： |
Canonical space Independence and identical distribution Peng’s law of
large numbers Sublinear expectation |
Classification： |
60A05, 60F05, 60E05, 60A86 |
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