Convergence to a self-normalized G-Brownian motion

Abstract

G-Brownian motion has a very rich and interesting new structure which nontrivially generalizes the classical one. Its quadratic variation process is also a continuous process with independent and stationary increments. We prove a self-normalized functional central limit theorem for independent and identically distributed random variables under the sub-linear expectation with the limit process being a G-Browian motion self-normalized by its quadratic variation. To prove the self-normalized central limit theorem, we also establish a new Donsker's invariance principle.

arXiv admin note: text overlap with arXiv:1503.02845

References in corpus (2)

• Rosenthal's inequalities for independent and negatively dependent random variables under sub-linear expectations with applications
• Donsker's invariance principle under the sub-linear expectation with an application to Chung's law of the iterated logarithm

Cited by in corpus (3)

• The convergence of the sums of independent random variables under the sub-linear expectations
• Lindeberg's central limit theorems for martingale like sequences under sub-linear expectations
• Strong law of large numbers for $m$-dependent and stationary random variables under sub-linear expectations