Tightness, weak compactness of nonlinear expectations and application to CLT
arXiv:1006.2541
Abstract
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.
11 pages
References in corpus (5)
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- Self-normalized moderate deviation and laws of the iterated logarithm under G-expectation
- Properties of solutions of stochastic differential equations driven by the G-Brownian motion
- Nonlinear Lévy Processes and their Characteristics
- The Independence under Sublinear Expectations
- Weak Approximation of G-Expectations
- Some Norm Estimates for Semimartingales
- Martingale Problem under Nonlinear Expectations
- Spatial and Temporal white noises under sublinear G-expectation
- Product space for two processes with independent increments under nonlinear expectations
- Generalized Wasserstein distance and weak convergence of sublinear expectations