Convergence to a self-normalized G-Brownian motion
Probability
2020-05-08 v2
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.
Cite
@article{arxiv.1507.07600,
title = {Convergence to a self-normalized G-Brownian motion},
author = {Li-Xin Zhang},
journal= {arXiv preprint arXiv:1507.07600},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1503.02845