Smooth density for some nilpotent rough differential equations
Probability
2013-12-19 v1
Abstract
In this note, we provide a non trivial example of differential equation driven by a fractional Brownian motion with Hurst parameter 1/3 < H < 1/2, whose solution admits a smooth density with respect to Lebesgue's measure. The result is obtained through the use of an explicit representation of the solution when the vector fields of the equation are nilpotent, plus a Norris type lemma in the rough paths context.
Cite
@article{arxiv.1104.1972,
title = {Smooth density for some nilpotent rough differential equations},
author = {Yaozhong Hu and Samy Tindel},
journal= {arXiv preprint arXiv:1104.1972},
year = {2013}
}
Comments
Contains a Norris type lemma in the rough paths context. A similar result is to be posted soon by M. Hairer and N. Pillai