Density of the signature process of fBm

Baudoin, Fabrice; Feng, Qi; Ouyang, Cheng

doi:10.1090/tran/8165

Density of the signature process of fBm
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by Fabrice Baudoin, Qi Feng and Cheng Ouyang PDF

Trans. Amer. Math. Soc. 373 (2020), 8583-8610 Request permission

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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