Electronic Journal of Probability

A support and density theorem for Markovian rough paths

Ilya Chevyrev and Marcel Ogrodnik

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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 proves a conjecture of Friz–Victoir [13]. 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.

Article information

Electron. J. Probab., Volume 23 (2018), paper no. 56, 16 pp.

Received: 24 August 2017
Accepted: 1 June 2018
First available in Project Euclid: 11 June 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60G17: Sample path properties

Markovian rough paths support in Hölder topology Hörmander’s theorem

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Chevyrev, Ilya; Ogrodnik, Marcel. A support and density theorem for Markovian rough paths. Electron. J. Probab. 23 (2018), paper no. 56, 16 pp. doi:10.1214/18-EJP184. https://projecteuclid.org/euclid.ejp/1528704074

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