Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations. (English) Zbl 1184.60009

Author’s 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 Ito’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.


60F25 \(L^p\)-limit theorems
60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
60G15 Gaussian processes
60E05 Probability distributions: general theory
60J65 Brownian motion
60H30 Applications of stochastic analysis (to PDEs, etc.)
Full Text: DOI


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