A support and density theorem for Markovian rough paths

Ilya Chevyrev, Marcel Ogrodnik

Research output: Contribution to journalArticlepeer-review

Abstract

We establish two results concerning a class of geometric rough paths X which arise as Markov processes associated to uniformly subelliptic Dirichlet forms. The first is a support theorem for X in α-Hölder rough path topology for all α∈(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 X, the proof of which is based on analysis of (non-symmetric) Dirichlet forms on manifolds.
Original languageEnglish
Article number56
Number of pages16
JournalElectronic journal of probability
Volume23
DOIs
Publication statusPublished - 11 Jun 2018

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