Normal approximation by Stein’s method under sublinear expectations

Yongsheng Song

Stochastic Processes and their Applications, 2020, vol. 130, issue 5, 2838-2850

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:

Keywords: Stein’s method; Normal approximation; Sublinear expectation; G-normal distribution (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2019.08.005

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