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2018 A support and density theorem for Markovian rough paths
Ilya Chevyrev, Marcel Ogrodnik
Electron. J. Probab. 23(none): 1-16 (2018). DOI: 10.1214/18-EJP184

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 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.

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Ilya Chevyrev. Marcel Ogrodnik. "A support and density theorem for Markovian rough paths." Electron. J. Probab. 23 1 - 16, 2018. https://doi.org/10.1214/18-EJP184

Information

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

zbMATH: 06924668
MathSciNet: MR3814250
Digital Object Identifier: 10.1214/18-EJP184

Subjects:
Primary: 60H10
Secondary: 60G17

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