Limit theorems with rate of convergence under sublinear expectations

2017/11/29 by Xiao Fang, Shige Peng, Fang, Xiao +5 · 3 citations
Mathematics · #60F05 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F05

paper · pdf · doi:10.48550/arxiv.1711.10649

34 pages

arxiv created 2018/05/15 · arxiv updated 2018/05/16

Abstract

Under the sublinear expectation 𝔼[⋅]:=sup_{θ∈ Θ} E_θ[⋅] for a given set of linear expectations \E_θ: θ∈ Θ\, we establish a new law of large numbers and a new central limit theorem with rate of convergence. We present some interesting special cases and discuss a related statistical inference problem. We also give an approximation and a representation of the G-normal distribution, which was used as the limit in Peng (2007)'s central limit theorem, in a probability space.

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• Probabilistic approximation of fully nonlinear second-order PIDEs with convergence rates for the universal robust limit theorem
• On nonlinear weak law of large numbers
• Limit theorems under nonlinear expectations dominated by sublinear expectations

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