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September  2021, 6(3): 199-212. doi: 10.3934/puqr.2021010

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

Yongsheng Song 1,2,

1. 

RCSDS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
2. 

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received  June 02, 2021 Accepted  August 20, 2021 Published  September 2021

Fund Project: 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).

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.

Keywords: Stein’s method, Rate of convergence, Law of large numbers.
Mathematics Subject Classification: 60F05, 60G50.
Citation: Yongsheng Song. Stein’s method for the law of large numbers under sublinear expectations. Probability, Uncertainty and Quantitative Risk, 2021, 6 (3) : 199-212. doi: 10.3934/puqr.2021010
References:
[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.

[2]

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

[3]

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.

[5]

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.

[6]

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

[7]

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.

show all references

References:
[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.

[2]

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

[3]

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.

[5]

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.

[6]

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

[7]

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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