Continuity in law with respect to the Hurst parameter of the local time of the fractional Brownian motion
Abstract
Description
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 $H_0$.
20 pages, submitted to Journal of Theoretical Probability
20 pages, submitted to Journal of Theoretical Probability