Limit theorems under nonlinear expectations dominated by sublinear expectations

2025/06/20 by Li, Xiaojuan, Hu, Mingshang
Economics, Econometrics and Finance · Decision Sciences · #Stochastic processes and financial applications #Probability and Risk Models #Financial Risk and Volatility Modeling

paper · pdf · doi:10.48550/arxiv.2506.17109

Abstract

In this paper, we obtain a new estimate for uniform integrability under sublinear expectations. Based on this, we establish the limit theorems under nonlinear expectations dominated by sublinear expectations through tightness, and the limit distributions can be completely nonlinear. Finally, we study the limit theorem in a special case, where the limit distribution satisfies positive homogeneity.

Citations

• Maximum principle for stochastic optimal control problem under convex expectation
• Functional central limit theorem with mean-uncertainty under sublinear expectation
• A robust α-stable central limit theorem under sublinear expectation without integrability condition
• Nonlinear semigroups and limit theorems for convex expectations
• A universal robust limit theorem for nonlinear Lévy processes under sublinear expectation
• A Central Limit Theorem for Sets of Probability Measures
• A monotone scheme for G-equations with application to the explicit convergence rate of robust central limit theorem
• On Shige Peng's central limit theorem
• Limit theorems with rate of convergence under sublinear expectations
• Normal Approximation by Stein's Method under Sublinear Expectations
• Tightness, weak compactness of nonlinear expectations and application to CLT
• Nonlinear Expectations and Stochastic Calculus under Uncertainty
• A New Central Limit Theorem under Sublinear Expectations
• Function spaces and capacity related to a Sublinear Expectation: application to G-Brownian Motion Pathes
• Law of Large Numbers and Central Limit Theorem under Nonlinear Expectations

Related

• Tightness, weak compactness of nonlinear expectations and application to CLT
• Limit theorems with rate of convergence under sublinear expectations
• Convergences of Random Variables under Sublinear Expectations
• Some inequalities and limit theorems under sublinear expectations
• Sublinear Expectations and Martingales in discrete time