Stein Type Characterization for G-normal Distributions

2016/03/15 by Hu, Mingshang, Peng, Shige, Song, Yongsheng
#35K55 #60A05 #60E05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1603.04611

Abstract

In this article, we provide a Stein type characterization for G-normal distributions: Let N[φ]=max_μ∈Θμ[φ], φ∈ C_b,Lip(ℝ), be a sublinear expectation. N is G-normal if and only if for any φ∈ C_b²(ℝ), we have ∫_ℝ[(x)/(2)φ'(x)-G(φ"(x))]μ^φ(dx)=0, where μ^φ is a realization of φ associated with N, i.e., μ^φ∈ Θ and μ^φ[φ]=N[φ].

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