Functional Shige Peng's central limit theorems for martingale vectors (Q6564807)

The author gives sufficient conditions for a functional central limit theorem (CLT) of random vectors in a sublinear expectation space with a multivariate G-Brownian motion (in the sense of Peng) in the limit. These conditions are concerned with the convergence of certain sums of conditional sublinear expectations. If the random vectors are independent in the sublinear expectation space, the author derives Lindeberg-type conditions and gives necessary and sufficient conditions for the functional CLT under the additional assumption on identical distribution. As an application of the main theorem, a Lévy-type characterization of the multivariate G-Brownian motion in terms of martingales is given.