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Convergence to a self-normalized G-Brownian motion

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.
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  • 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.
    Mathematics Subject Classification: 60F15;60F05;60H10;60G48.


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