Central limit theorems for bounded random variables under belief measures

DOI10.1016/j.jmaa.2017.11.019zbMath1392.60029arXiv1501.00771OpenAlexW2770868878MaRDI QIDQ681767

Xiao-Min Shi

Publication date: 13 February 2018

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.00771

zbMATH Keywords

central limit theoremnon-additive measurebelief measure

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Stochastic analysis (60H99)

Cites Work

• Unnamed Item
• Unnamed Item
• A general central limit theorem under sublinear expectations
• Exchangeable capacities, parameters and incomplete theories
• Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations
• Towards a frequentist theory of upper and lower probability
• Limit laws for non-additive probabilities and their frequentist interpretation
• IID: Independently and indistinguishably distributed.
• A strong law of large numbers for capacities
• Multi-dimensional central limit theorems and laws of large numbers under sublinear expectations
• A strong law of large numbers for non-additive probabilities
• Ambiguous volatility, possibility and utility in continuous time
• Multi-dimensional \(G\)-Brownian motion and related stochastic calculus under \(G\)-expectation
• Minimax tests and the Neyman-Pearson lemma for capacities
• Theory of capacities
• A Weighted Central Limit Theorem Under Sublinear Expectations
• General laws of large numbers under sublinear expectations
• Risk, Ambiguity, and the Savage Axioms
• Robust Confidence Regions for Incomplete Models
• Decision Making with Monotone Lower Probabilities of Infinite Order
• Le Comportement de l'Homme Rationnel devant le Risque: Critique des Postulats et Axiomes de l'Ecole Americaine