摘要
The main achievement of this paper is the finding and proof of Central Limit Theorem(CLT,see Theorem 12)under the framework of sublinear expectation.Roughly speaking under some reasonable assumption,the random sequence{1/√n(X1+···+Xn)}i∞=1 converges in law to a nonlinear normal distribution,called G-normal distribution,where{Xi}i∞=1 is an i.i.d.sequence under the sublinear expectation.It’s known that the framework of sublinear expectation provides a important role in situations that the probability measure itself has non-negligible uncertainties.Under such situation,this new CLT plays a similar role as the one of classical CLT.The classical CLT can be also directly obtained from this new CLT,since a linear expectation is a special case of sublinear expectations.A deep regularity estimate of 2nd order fully nonlinear parabolic PDE is applied to the proof of the CLT.This paper is originally exhibited in arXiv.(math.PR/0702358v1).
