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Stein’s method for the law of large numbers under sublinear expectations

This research is supported by the National Key R&D Program of China (Grant Nos. 2020YFA0712700, 2018YFA0703901); National Natural Science Foundation of China (Grant Nos.11871458, 11688101) and Key Research Program of Frontier Sciences, CAS (Grant No. QYZDB-SSW-SYS017).
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  • Peng, S. [6] proved the law of large numbers under a sublinear expectation. In this paper, we give its error estimates by Stein’s method.

    Mathematics Subject Classification: 60F05, 60G50.


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  • [1]

    Denis, L., Hu, M. and Peng, S., Function spaces and capacity related to a sublinear expectation: application to G-Brownian motion paths, Potential Anal., 2011, 34: 139-161.doi: 10.1007/s11118-010-9185-x.


    Fang, X., Peng, S., Shao, Q. and Song Y., Limit theorems with rate of convergence under sublinear expectations, Bernoulli, 2019, 25(4A): 2564-2596.


    Hu, M., Peng S. and Song, Y., Stein type characterization for G-normal distributions, Electron. Commun. Probab., 2017, 22(24): 1-12.

    [4] Krylov, N. V., Nonlinear Parabolic and Elliptic Equations of the Second Order, Reidel Publishing Company, (Original Russian Version by Nauka, Moscow, 1985), 1987.

    Krylov, N. V., On Shige Peng’s central limit theorem, Stochastic Process. Appl., 2020, 130(3): 1426-1434.doi: 10.1016/j.spa.2019.05.005.


    Peng, S., Law of large numbers and central limit theorem under nonlinear expectations, Probab. Uncertain. Quant. Risk, 2019, 4(4): 8.


    Song,Y., Normal approximation by Stein’s method under sublinear expectations, Stochastic Process. Appl., 2020, 130(5): 2838-2850.doi: 10.1016/j.spa.2019.08.005.

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