A New Central Limit Theorem under Sublinear Expectations

2008/03/18 by Shigē Péng, Shige Peng, Peng, Shige · 13 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #60H05 #60H10 #60H30 #FOS: Mathematics #Probability (math.PR) #Risk and Portfolio Optimization #Statistical Mechanics and Entropy #Statistics Theory (math.ST) #Stochastic processes and financial applications #math.PR #math.ST #msc:60H05 #msc:60H10 #msc:60H30 #stat.TH

paper · pdf · doi:10.48550/arxiv.0803.2656

arxiv created 2008/03/18 · openalex publication_date 2008/03/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that mean-uncertainty can be also described. W present our new result of central limit theorem under sublinear expectation. This theorem can be also regarded as a generalization of the law of large number in the case of mean-uncertainty.

Citations

• G-Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty
• Law of Large Numbers and Central Limit Theorem under Nonlinear Expectations
• Function spaces and capacity related to a Sublinear Expectation: application to G-Brownian Motion Pathes

Cited by

• Regularity of Solutions of Mean-Field G-SDEs
• Asymptotic Optimality in Data-Driven Decision Making
• Limit theorems under nonlinear expectations dominated by sublinear expectations
• On the Law of the Iterated Logarithm for m-dependent stationary random variables under sub-linear expectations
• Gradient Estimates for Nonlinear Diffusion Semigroups by Coupling Methods
• General laws of large numbers under sublinear expectations
• Explicit solutions of G-heat equation with a class of initial conditions by G-Brownian motion
• Robust valuation and risk measurement under model uncertainty
• G-Gaussian Processes under Sublinear Expectations and q-Brownian Motion in Quantum Mechanics
• Stein Type Characterization for G-normal Distributions
• Moment bounds for IID sequences under sublinear expectations
• On the laws of the iterated logarithm under sub-linear expectations
• Product space for two processes with independent increments under nonlinear expectations

Related

• Law of Large Numbers and Central Limit Theorem under Nonlinear Expectations
• Limit theorems with rate of convergence under sublinear expectations
• Normal Approximation by Stein's Method under Sublinear Expectations
• Functional central limit theorem with mean-uncertainty under sublinear expectation
• A weighted central limit theorem under sublinear expectations