Lindeberg's central limit theorems for martingale-like sequences under sub-linear expectations

• 作者: Li-Xin Zhang
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2021,（6）
• 所属期刊栏目: Articles
• 页码范围: 1263-1290
• 页数: 28页
• 语种: 英文

摘要

The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes,especially stochastic integrals and differential equations.In this paper,the central limit theorem and the functional central limit theorem are obtained for martingale-like random variables under the sub-linear expectation.As applications,the Lindeberg's central limit theorem is obtained for independent but not necessarily identically distributed random variables,and a new proof of the Lévy characterization of a G-Brownian motion without using stochastic calculus is given.For proving the results,Rosenthal's inequality and the exponential inequality for the martingale-like random variables are established.