Tightness, weak compactness of nonlinear expectations and application to CLT

Details Tightness, weak compactness of nonlinear expectations and application to CLT Tightness, weak compactness of nonlinear expectations and application to CLT

2010-06-13

arxiv.org/abs/1006.2541v1

Mathematics

Probability

11 pages

Scientific paper

In this paper we introduce a notion of tightness for a family of nonlinear expectations and show that the tightness can be applied to obtain weak compactness in a framework of nonlinear expectation space. This criterion is very useful for obtaining the weak convergence for a sequence of nonlinear expectations, which is a equivalent to the so-called convergence in distribution, or in law for a sequence of random variables in a nonlinear expectation space. We use the above result to give a new proof to the central limit theorem under a sublinear expectation space. The method can be also applied to prove the convergence of some numerical schemes for degenerate fully nonlinear PDEs.

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