A support and density theorem for Markovian rough paths

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 $\alpha$-Hölder rough path topology for all $\alpha \in (0,1/2)$, 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.

17 pages. Added several clarifications. To appear in Electron. J. Probab

References in corpus (1)

• Random walks and Lévy processes as rough paths

Cited by in corpus (3)

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• Random walks and Lévy processes as rough paths
• A Version of Hörmander's Theorem for Markovian Rough Paths