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

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Nonlinear Expectations and Stochastic Calculus under Uncertainty (2010, background): “Hu and Peng (2009) [58] then have introduced an intrinsic and simple approach.”
Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications (2011, methodology): “The following result was established in Denis, Hu and Peng (2008), a simpler and more direct argument was then obtained in Hu and Peng (2009a).”
Comparison Theorem, Feynman-Kac Formula and Girsanov Transformation for BSDEs Driven by G-Brownian Motion (2012, background): “1 Introduction Recently, Peng systemically established a time-consistent fully nonlinear expectation theory (see [17], [18] and [23]).”
A law of the iterated logarithm under sublinear expectations (2011, background): “ An ↓ A, where An,A ∈ F. Lawofiteratedlogarithm 4 Because we investigate LIL for capacity, the notion of IID random variables under sub-linear expectations introduced by Peng is changed slightly ( cf.[12, 13, 14, 15, 16]). Deﬁnition 3 (IID under sublinear expectations) Independence: Suppose that Y1,”
Strong laws of large numbers for capacities (2010, background): “Recently, motivated by the risk measures, super-hedge pricing and modelling uncertainty in finance, Peng [11,12,13,14,15] initiated the notion of independent and identically distributed (IID) random variables under sub-linear expectations.”