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 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 X, the proof of which is based on analysis of (non-symmetric) Dirichlet forms on manifolds.
A support and density theorem for Markovian rough paths / Chevyrev, Ilya; Ogrodnik, Marcel. - In: ELECTRONIC JOURNAL OF PROBABILITY. - ISSN 1083-6489. - 23:none(2018), pp. 1-16. [10.1214/18-ejp184]
A support and density theorem for Markovian rough paths
Chevyrev, Ilya;
2018-01-01
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 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 X, the proof of which is based on analysis of (non-symmetric) Dirichlet forms on manifolds.| File | Dimensione | Formato | |
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