• Corpus ID: 248496861

Wasserstein Asymptotics for the Empirical Measure of Fractional Brownian Motion on a Flat Torus

@inproceedings{Huesmann2022WassersteinAF,
  title={Wasserstein Asymptotics for the Empirical Measure of Fractional Brownian Motion on a Flat Torus},
  author={Martin Huesmann and Francesco Mattesini and Dario Trevisan},
  year={2022}
}
. We establish asymptotic upper and lower bounds for the Wasserstein distance of any order p ≥ 1 between the empirical measure of a fractional Brownian motion on a flat torus and the uniform Lebesgue measure. Our inequalities reveal an interesting interaction between the Hurst index H and the dimension d of the state space, with a “phase-transition” in the rates when d = 2 + 1 /H , akin to the Ajtai-Koml´os-Tusn´ady theorem for the optimal matching of i.i.d. points in two-dimensions. Our proof… 

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TLDR
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