Limit theorems with rate of convergence under sublinear expectations

2017/11/29 by Fang, Xiao, Peng, Shige, Shao, Qi-Man +1 · 3 citations
#60F05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1711.10649

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.

Cited by

• 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

Related

• Convergence rates in the law of large numbers under sublinear expectations
• A New Central Limit Theorem under Sublinear Expectations
• Almost Sure Central Limit Theorem in Sub-linear Expectation Spaces
• Law of Large Numbers and Central Limit Theorem under Nonlinear Expectations
• Normal Approximation by Stein's Method under Sublinear Expectations