Density of the signature process of fBm

2019/04/20 by Baudoin, Fabrice, Feng, Qi, Ouyang, Cheng · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1904.09384

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.

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