A support and density theorem for Markovian rough paths

被引：2

作者：

Chevyrev, Ilya ^{[1
]}

Ogrodnik, Marcel ^{[2
]}

机构：

[1] Univ Oxford, Oxford, England

[2] Imperial Coll London, Oxford, England

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2018年 / 23卷

关键词：

Markovian rough paths; support in Holder topology; Hormander's theorem; UNIFORMLY SUBELLIPTIC OPERATORS; DIFFERENTIAL-EQUATIONS; CONTINUITY;

D O I：

10.1214/18-EJP184

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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 alpha-Holder rough path topology for all alpha is an element of (0,1/2), which proves a conjecture of Friz-Victoir [13]. The second is a Hormander-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.

引用

页数：16

共 24 条

[1]

Agrachev Andrei A., 2004, ENCYCL MATH SCI, V87

[2]

[Anonymous], 2011, DEGRUYTER STUDIES MA

[3] Extending the Wong-Zakai theorem to reversible Markov processes [J].