Continuity in law with respect to the Hurst parameter of the local time of the fractional Brownian motion

Maria Jolis, Noèlia Viles

Published 2007-02-12Version 1

We give a result of stability in law of the local time of the fractional Brownian motion with respect to small perturbations of the Hurst parameter. Concretely, we prove that the law (in the space of continuous functions) of the local time of the fractional Brownian motion with Hurst parameter $H$ converges weakly to that of the local time of $B^{H_0}$, when $H$ tends to $H_0$.