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Backward stochastic differential equations with Young drift
January  2017, 2: 4 doi: 10.1186/s41546-017-0013-8

## Convergence to a self-normalized G-Brownian motion

 School of Mathematical Sciences, Zhejiang University, Hangzhou 310027 China

Received  October 25, 2016 Revised  January 05, 2017 Published  June 2017

Fund Project: supported by Grants from the National Natural Science Foundation of China (No. 11225104), the 973 Program (No. 2015CB352302) and the Fundamental Research Funds for the Central Universities.

G-Brownian motion has a very rich and interesting new structure that nontrivially generalizes the classical Brownian motion. 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-Brownian motion self-normalized by its quadratic variation. To prove the self-normalized central limit theorem, we also establish a new Donsker's invariance principle with the limit process being a generalized G-Brownian motion.
Citation: Zhengyan Lin, Li-Xin Zhang. Convergence to a self-normalized G-Brownian motion. Probability, Uncertainty and Quantitative Risk, 2017, 2 (0) : 4-. doi: 10.1186/s41546-017-0013-8
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