A Weighted Central Limit Theorem Under Sublinear Expectations

DOI10.1080/03610926.2012.665557zbMath1398.60044arXiv1105.0727OpenAlexW2046315308MaRDI QIDQ2815385

Defei Zhang, Zeng-Jing Chen

Publication date: 28 June 2016

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.0727

zbMATH Keywords

central limit theoremsublinear expectationsG-distributedweighted sum of independent random variables

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Functional limit theorems; invariance principles (60F17)

Related Items (9)

Central limit theorems for sub-linear expectation under the Lindeberg condition ⋮ Large deviation principle for random variables under sublinear expectations on \(\mathbb{R}^d\) ⋮ Complete integral convergence for weighted sums of widely negative dependent random variables under the sub-linear expectations ⋮ Central limit theorems for bounded random variables under belief measures ⋮ An \(\alpha\)-stable limit theorem under sublinear expectation ⋮ Complete convergence for weighted sums of widely acceptable random variables under sublinear expectations ⋮ Large deviation for negatively dependent random variables under sublinear expectation ⋮ Some types of convergence for negatively dependent random variables under sublinear expectations ⋮ Multi-dimensional central limit theorems and laws of large numbers under sublinear expectations

Cites Work

• Optimal stopping for non-linear expectations. I
• Optimal stopping for non-linear expectations. II
• Martingale representation theorem for the \(G\)-expectation
• Properties of hitting times for \(G\)-martingales and their applications
• Large deviations for stochastic differential equations driven by \(G\)-Brownian motion
• Central limit theorem for capacities
• Function spaces and capacity related to a sublinear expectation: application to \(G\)-Brownian motion paths
• A general central limit theorem under sublinear expectations
• Martingale characterization of \(G\)-Brownian motion
• The minimal sublinear expectations and their related properties
• Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations
• Limiting behavior of weighted sums of independent random variables

This page was built for publication: A Weighted Central Limit Theorem Under Sublinear Expectations