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arXiv · 1701.03002

A support and density theorem for Markovian rough paths

Ilya Chevyrev·Marcel Ogrodnik
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Abstract

We establish two results concerning a class of geometric rough paths $\mathbf{X}$ which arise as Markov processes associated to uniformly subelliptic Dirichlet forms. The first is a support theorem for $\mathbf{X}$ in $α$-Hölder rough path topology for all $α\in (0,1/2)$, which answers in the positive a conjecture of Friz-Victoir (2010). The second is a Hörmander-type theorem for the existence of a density of a rough differential equation driven by $\mathbf{X}$, the proof of which is based on analysis of (non-symmetric) Dirichlet forms on manifolds.

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Ilya Chevyrev, Marcel Ogrodnik. 2018-06-01. A support and density theorem for Markovian rough paths. https://doi.org/10.1214/18-ejp184

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