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An Algebraic Approach to Integration of Geometric Rough Paths

  • Danyu Yang
Conference paper
Part of the Abel Symposia book series (ABEL, volume 13)

Abstract

We build a connection between rough path theory and a non-commutative algebra, and interpret the integration of geometric rough paths as an example of a non-abelian Young integration. We identify a class of slowly-varying one-forms, and prove that the class is stable under basic operations.

Notes

Acknowledgements

The author would like to express sincere gratitude to Prof. Terry Lyons for numerous inspiring discussions that eventually lead to this paper. The author also would like to thank Prof. Martin Hairer, Sina Nejad, Dr. Horatio Boedihardjo, Dr. Xi Geng, Dr. Ilya Chevyrev and Vlad Margarint for discussions and suggestions on (an earlier version of) the paper, and thank Prof. Kurusch Ebrahimi-Fard and anonymous referees for constructive suggestions.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNTNUTrondheimNorway

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