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How big are the increments of G-Brownian motion?

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Abstract

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).

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, China

    Feng Hu

  2. School of Mathematics, Shandong University, Jinan, 250100, China

    ZengJing Chen

  3. Department of Financial Engineering, Ajou University, Suwon, 443-749, Korea

    ZengJing Chen

  4. Department of Mathematics, Honghe University, Mengzi, 661100, China

    DeFei Zhang

Authors
  1. Feng Hu
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  2. ZengJing Chen
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  3. DeFei Zhang
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Correspondence to Feng Hu.

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Hu, F., Chen, Z. & Zhang, D. How big are the increments of G-Brownian motion?. Sci. China Math. 57, 1687–1700 (2014). https://doi.org/10.1007/s11425-014-4816-0

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  • DOI: https://doi.org/10.1007/s11425-014-4816-0

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