2021
DOI: 10.3934/puqr.2021010
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Stein’s method for the law of large numbers under sublinear expectations

Abstract: <p style='text-indent:20px;'>Peng, S. [<xref ref-type="bibr" rid="b6">6</xref>] proved the law of large numbers under a sublinear expectation. In this paper, we give its error estimates by Stein’s method. </p>

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Cited by 8 publications
(4 citation statements)
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“…(2.9) and (2.10) tell us that, if the condition (CC) is satisfied, then with capacity 1 under the upper capacity V * , when n → ∞, the number S n /n can take any value inside [µ, µ] and (2.2) remains true as Peng [12,13] claimed. Song [16] has shown (2.8) and (2.10)…”
Section: The Main Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…(2.9) and (2.10) tell us that, if the condition (CC) is satisfied, then with capacity 1 under the upper capacity V * , when n → ∞, the number S n /n can take any value inside [µ, µ] and (2.2) remains true as Peng [12,13] claimed. Song [16] has shown (2.8) and (2.10)…”
Section: The Main Resultsmentioning
confidence: 99%
“…. ), Song [16] has also shown that for every finite-dimensional Borel-measurable function ϕ(x 1 , . .…”
Section: The Main Resultsmentioning
confidence: 99%
“…Remark 2.11 Recently, Fang et al [4], Song [17] and Hu et al [7] obtained the convergence rate of (7) under higher moment conditions. If we further assume that Ê[X 2 1 ] < ∞ in Theorem 2.10, then we have…”
Section: Preliminaries Of Sublinear Expectation Theorymentioning
confidence: 99%
“…Song (2020) ( [12]) established Stein's method under sublinear expectations based on the regularity results of fully nonlinear PDEs given in [6]. Recently, using Stein's method, Song (2021) ( [13]) provided the following error estimate for the wLLN*:…”
Section: Introductionmentioning
confidence: 99%