Malliavin calculus for fractional delay equations
Probability
2009-12-14 v1
Abstract
In this paper we study the existence of a unique solution to a general class of Young delay differential equations driven by a H\"older continuous function with parameter greater that 1/2 via the Young integration setting. Then some estimates of the solution are obtained, which allow to show that the solution of a delay differential equation driven by a fractional Brownian motion (fBm) with Hurst parameter H>1/2 has a smooth density. To this purpose, we use Malliavin calculus based on the Frechet differentiability in the directions of the reproducing kernel Hilbert space associated with fBm.
Cite
@article{arxiv.0912.2180,
title = {Malliavin calculus for fractional delay equations},
author = {Jorge A. Leon and Samy Tindel},
journal= {arXiv preprint arXiv:0912.2180},
year = {2009}
}