How big are the increments of \(G\)-Brownian motion?
The limit theory of Brownian motion plays an important role in the development of probability theory and its applications. This paper considers the limit theory of \(G\)-Brownian motion, more precisely, considers the problem: How big are the increments of \(G\)-Brownian motion. The authors obtain the Csörgő and Révész type theorem of the increments of \(G\)-Brownian motion and get, as applications of the result, the law of iterated logarithm and the Erdős and Rényi law of large numbers for \(G\)-Brownian motion. These results extend the classical results obtained in [\textit{M. Csörgő} and \textit{P. Revesz}, Ann. Probab. 7, 731--737 (1979; Zbl 0412.60038)].
scientific article; zbMATH DE number 6376163
scientific article