On the Fourier dimension of fractional Brownian graphs
Abstract
In this note we prove that the Fourier dimension of the graph G(B) of a fractional Brownian motion B with Hurst parameter H∈(0,1/2) is equal to 1. This finishes to solve a conjecture by Fraser and Sahlsten. It also yields an exact formula for the gap H(G(B)) - F(G(B)) between the Hausdorff dimension and the Fourier dimension of G(B). The proof is based on an intricate combinatorics procedure for multiple integrals related to the covariance function of the fractional Brownian motion.
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