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Stochastic calculus with respect to G-Brownian motion viewed through rough paths

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Abstract

We study rough path properties of stochastic integrals of Itô’s type and Stratonovich’s type with respect to G-Brownian motion. The roughness of G-Brownian motion is estimated and then the pathwise Norris lemma in G-framework is obtained.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 10921101) and the Programme of Introducing Talents of Discipline to Universities of China (Grant No. B12023). The authors thank valuable suggestions of Dr. Falei Wang to this paper.

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Authors and Affiliations

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

    ShiGe Peng

  2. Institute for Advanced Research, Shandong University, Jinan, 250100, China

    HuiLin Zhang

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  1. ShiGe Peng
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  2. HuiLin Zhang
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Correspondence to ShiGe Peng.

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Dedicated to Professor LI TaTsien on the Occasion of His 80th Birthday

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Peng, S., Zhang, H. Stochastic calculus with respect to G-Brownian motion viewed through rough paths. Sci. China Math. 60, 1–20 (2017). https://doi.org/10.1007/s11425-016-0171-4

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  • DOI: https://doi.org/10.1007/s11425-016-0171-4

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