2010/06/13 by Shigē Péng, Shi-Ge Peng, Peng, Shi-Ge · 7 citations
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #Optimization and Variational Analysis #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.PR #msc:60-00
paper · pdf · doi:10.48550/arxiv.1006.2541
11 pages
arxiv created 2010/06/13 · arxiv updated 2010/06/15
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.