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Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations

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Abstract

This is a survey on normal distributions and the related central limit theorem under sublinear expectation. We also present Brownian motion under sublinear expectations and the related stochastic calculus of Itô’s type. The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk, statistics and other industrial problems.

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Authors and Affiliations

  1. Institute of Mathematics, Shandong University, Jinan, 250100, China

    ShiGe Peng

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  1. ShiGe Peng
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Correspondence to ShiGe Peng.

Additional information

This work was partially supported by National Basic Research Program of China (Grant No. 2007CB814900) (Financial Risk)

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Peng, S. Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations. Sci. China Ser. A-Math. 52, 1391–1411 (2009). https://doi.org/10.1007/s11425-009-0121-8

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  • DOI: https://doi.org/10.1007/s11425-009-0121-8

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