Limit theorems with rate of convergence under sublinear expectations

Abstract

Under the sublinear expectation $\mathbb{E}[\cdot ]:={\sup }_{\theta \in \Theta }{E}_{\theta }[\cdot ]$ for a given set of linear expectations $\{E_{\theta }:\theta \in \Theta \}$, 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.

34 pages

Cited by in corpus (2)

• Stein's Method for Law of Large Numbers under Sublinear Expectations
• A hypothesis-testing perspective on the G-normal distribution theory