In this paper,we investigate the problem:How big are the increments of G-Brownian motion.We obtain the Csrg and R′ev′esz’s type theorem for the increments of G-Brownian motion.As applications of this result,we get the law of iterated logarithm and the Erds and R′enyi law of large numbers for G-Brownian motion.Furthermore,it turns out that our theorems are natural extensions of the classical results obtained by Csrg and R′ev′esz(1979).
In this paper, we study dynamically consistent nonlinear evaluations in Lp （1 〈 p 〈 2）. One of our aim is to obtain the following result： under a domination condition, an Ft-consistent evaluation is an Sg-evaluation in Lp. Furthermore, without the assumption that the generating function g（t, w, y, z） is continuous with respect to t, we provide some useful characterizations of an εg-evaluation by g and give some applications. These results include and extend some existing results.
