Functional Shige Peng’s Central Limit Theorems for Martingale Vectors

Abstract

In this paper, the functional central limit theorem is established for martingale like random vectors under the framework sub-linear expectations introduced by Shige Peng. As applications, the Lindeberg central limit theorem for independent random vectors is established, the sufficient and necessary conditions of the central limit theorem for independent and identically distributed random vectors are found, and a Lévy’s characterization of a multi-dimensional G-Brownian motion is obtained.

Keywords

Random vector / Central limit theorem / Functional central limit theorem / Martingale difference / Sub-linear expectation

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Funding

National Natural Science Foundation of China(11731012)

Fundamental Research Funds for the Central Universities

Natural Science Foundation of Zhejiang Province(LZ21A010002)