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Normal approximation by Stein’s method under sublinear expectations

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  • Song, Yongsheng

Abstract

Peng (2008) proved the Central Limit Theorem under a sublinear expectation: Let(Xi)i≥1be a sequence of i.i.d random variables under a sublinear expectationEˆwithEˆ[X1]=Eˆ[−X1]=0andEˆ[|X1|3]<∞. SettingWn≔X1+⋯+Xnn, we have, for each bounded Lipschitz functionφ,limn→∞|Eˆ[φ(Wn)]−NG(φ)|=0,whereNGis theG-normal distribution withG(a)=12Eˆ[aX12],a∈R In this paper, we shall give an estimate of the convergence rate of this CLT by Stein’s method under sublinear expectations:

Suggested Citation

  • Song, Yongsheng, 2020. "Normal approximation by Stein’s method under sublinear expectations," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2838-2850.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:5:p:2838-2850
    DOI: 10.1016/j.spa.2019.08.005
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    References listed on IDEAS

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    1. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
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