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2017 Stein type characterization for $G$-normal distributions
Mingshang Hu, Shige Peng, Yongsheng Song
Electron. Commun. Probab. 22: 1-12 (2017). DOI: 10.1214/17-ECP53

Abstract

In this article, we provide a Stein type characterization for $G$-normal distributions: Let $\mathcal{N} [\varphi ]=\sup _{\mu \in \Theta }\mu [\varphi ],\ \varphi \in C_{b,Lip}(\mathbb{R} ),$ be a sublinear expectation. $\mathcal{N} $ is $G$-normal if and only if for any $\varphi \in C_b^2(\mathbb{R} )$, we have \[ \int _\mathbb{R} [\frac{x} {2}\varphi '(x)-G(\varphi ''(x))]\mu ^\varphi (dx)=0, \] where $\mu ^\varphi $ is a realization of $\varphi $ associated with $\mathcal{N} $, i.e., $\mu ^\varphi \in \Theta $ and $\mu ^\varphi [\varphi ]=\mathcal{N} [\varphi ]$.

Citation

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Mingshang Hu. Shige Peng. Yongsheng Song. "Stein type characterization for $G$-normal distributions." Electron. Commun. Probab. 22 1 - 12, 2017. https://doi.org/10.1214/17-ECP53

Information

Received: 26 April 2016; Accepted: 4 April 2017; Published: 2017
First available in Project Euclid: 19 April 2017

zbMATH: 1370.60020
MathSciNet: MR3645506
Digital Object Identifier: 10.1214/17-ECP53

Subjects:
Primary: 35K55, 60A05, 60E05

JOURNAL ARTICLE
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