How big are the increments of G-Brownian motion?

• DOI: 10.1007/s11425-014-4816-0
• Publication Date: 2014-05-08T04:47:55Z
• Authors: Feng Hu; ZengJing Chen; DeFei Zhang
• Keywords: Iterated logarithm; Iterated function; Fractional Brownian motion; Natural logarithm; Reflected Brownian motion

In this paper, we investigate the problem: How big are the increments of G-Brownian motion. We obtain the Csorgő and Revesz’s type theorem for the increments of G-Brownian motion. As applications of this result, we get the law of iterated logarithm and the Erdős and Renyi law of large numbers for G-Brownian motion. Furthermore, it turns out that our theorems are natural extensions of the classical results obtained by Csorgő and Revesz (1979).