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Abstract: In this paper we introduce a notion of tightness for a family of nonlinearexpectations and show that the tightness can be applied to obtain weakcompactness in a framework of nonlinear expectation space. This criterion isvery useful for obtaining the weak convergence for a sequence of nonlinearexpectations, which is a equivalent to the so-called convergence indistribution, or in law for a sequence of random variables in a nonlinearexpectation space. We use the above result to give a new proof to the centrallimit theorem under a sublinear expectation space. The method can be alsoapplied to prove the convergence of some numerical schemes for degenerate fullynonlinear PDEs.



Autor: Shi-Ge Peng

Fuente: https://arxiv.org/







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