Hölder-Continuous Rough Paths by Fourier Normal Ordering

@article{Unterberger2010HlderContinuousRP,
  title={H{\"o}lder-Continuous Rough Paths by Fourier Normal Ordering},
  author={J'er'emie Unterberger},
  journal={Communications in Mathematical Physics},
  year={2010},
  volume={298},
  pages={1-36}
}
  • J'er'emie Unterberger
  • Published 2010
  • Mathematics, Physics
  • Communications in Mathematical Physics
  • We construct in this article an explicit geometric rough path over arbitrary d-dimensional paths with finite 1/α-variation for any $${\alpha\in(0,1)}$$. The method may be coined as ‘Fourier normal ordering’, since it consists in a regularization obtained after permuting the order of integration in iterated integrals so that innermost integrals have highest Fourier frequencies. In doing so, there appear non-trivial tree combinatorics, which are best understood by using the structure of the Hopf… CONTINUE READING

    Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

    Citations

    Publications citing this paper.
    SHOWING 1-10 OF 10 CITATIONS

    A Renormalized Rough Path over Fractional Brownian Motion

    VIEW 5 EXCERPTS
    CITES BACKGROUND & METHODS
    HIGHLY INFLUENCED

    Ordered forests, permutations and iterated integrals

    VIEW 5 EXCERPTS
    CITES BACKGROUND & METHODS
    HIGHLY INFLUENCED

    Dynamical invariance for random matrices

    VIEW 1 EXCERPT
    CITES METHODS