Science China Mathematics

, Volume 57, Issue 8, pp 1687–1700 | Cite as

How big are the increments of G-Brownian motion?

  • Feng HuEmail author
  • ZengJing Chen
  • DeFei Zhang


In this paper, we investigate the problem: How big are the increments of G-Brownian motion. We obtain the Csörgő and Révész’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 Rényi law of large numbers for G-Brownian motion. Furthermore, it turns out that our theorems are natural extensions of the classical results obtained by Csörgő and Révész (1979).


sublinear expectation capacity G-normal distribution G-Brownian motion increments of G-Brownian motion law of iterated logarithm 


60H10 60G48 


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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Mathematical SciencesQufu Normal UniversityQufuChina
  2. 2.School of MathematicsShandong UniversityJinanChina
  3. 3.Department of Financial EngineeringAjou UniversitySuwonKorea
  4. 4.Department of MathematicsHonghe UniversityMengziChina

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