Malliavin calculus for fractional delay equations

Details Malliavin calculus for fractional delay equations Malliavin calculus for fractional delay equations

2009-12-11

arxiv.org/abs/0912.2180v1

Mathematics

Probability

Scientific paper

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.

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