%0 Journal Article
%T Malliavin calculus for fractional delay equations
%A Jorge A. Leon
%A Samy Tindel
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0912.2180v1