On the slow points of fractional Brownian motion

Abstract

Esser and Loosveldt have recently resolved a long-standing open problem in the folklore by proving that fractional Brownian motion (fBm) has slow points in the sense of Kahane, following a rich theory of slow points developed for Brownian motion and other, related, self-similar Markov processes. We presently introduce another method for the study of slow points in order to compute the Hausdorff dimension of fBm slow points. Our method follows recent ideas on the points of slow growth for SPDEs but also requires a number of new localization ideas that are likely to have other applications.