Francesco Mattesini (MPI MIS, Leipzig + University of Munster)
Wednesday, October 27, 2021 - 11:00
MPI fur Mathematik in den Naturwissenschaften Leipzig
Inselstr. 22, 04103 Leipzig, E1 05 (Leibniz-Saal), 1. Etage
We establish sharp upper and lower bounds for the Kantorovich optimal transport distance between the uniform measure and the occupation measure of a path of a fractional Brownian motion with Hurst index H taking values in a d-dimensional torus. Similar problems have been recently studied for diffusion processes taking values on a compact connected Riemmanian manifold. We give new insights in the case of fractional Brownian motion taking care of the absence of the Markovian structure by means of recently introduced PDE techniques and compare our result with the ones already known. In particular we show that a phase transition between rates occurs if d=1/H +2, in analogy with the random Euclidean bipartite matching problem, i.e. when the occupation measure is replaced by i.i.d. uniform points (formally given by infinite H).

Joint work with M. Huesmann (WWU Munster) and D. Trevisan (Universita degli studi di Pisa)

submitted by Katja Heid (Katja.Heid@mis.mpg.de, 0341 9959 50)