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arxiv: 1904.09384 · v1 · pith:SKMA2M6Xnew · submitted 2019-04-20 · 🧮 math.PR

Density of the signature process of fBm

Fabrice Baudoin , Qi Feng , Cheng Ouyang This is my paper
classification 🧮 math.PR
keywords densitysignatureasymptoticsboundsbrowniancarnot-carathcontrolleddistance
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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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  1. Precise Local Estimates for Hypoelliptic Differential Equations driven by Fractional Brownian Motions

    math.PR 2019-06 unverdicted novelty 6.0

    The authors establish sharp local estimates for the control distance and density lower bounds in hypoelliptic rough differential equations driven by fractional Brownian motion with H > 1/4.