Density of the signature process of fBm

Fabrice Baudoin; Qi Feng; Cheng Ouyang

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arXiv · 1904.09384

Density of the signature process of fBm

Fabrice Baudoin·Qi Feng·Cheng Ouyang

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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-Carath\'eodory distance of the group.

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Fabrice Baudoin, Qi Feng, Cheng Ouyang. 2019-04-20. Density of the signature process of fBm. https://arxiv.org/abs/1904.09384

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