Density of the signature process of fBm

Abstract

We study the density of the signature of fractional Brownian motions with parameter $H>1/4$. In particular, we prove existence, smoothness, global Gaussian upper bounds and Varadhan's type asymptotics for this density. A key result is that the estimates on the density we obtain are controlled by the Carnot-Carathéodory distance of the group.

28 pages

References in corpus (1)

• Large deviations for rough paths of the fractional Brownian motion

Cited by in corpus (1)

• Precise Local Estimates for Hypoelliptic Differential Equations driven by Fractional Brownian Motions