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

Yongsheng Song

doi:10.3934/puqr.2021010

Article Contents

2021, Volume 6, Issue 3: 199-212. Doi: 10.3934/puqr.2021010

This issue Previous Article Optimal unbiased estimation for maximal distribution Next Article Stochastic maximum principle for systems driven by local martingales with spatial parameters

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 2021

Accepted: August 19, 2021

Published: September 2021

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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Abstract

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.

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Mathematics Subject Classification: 60F05, 60G50.

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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.