A singular stochastic differential equation driven by fractional Brownian motion

In this paper we study a singular stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter H>12. Under some assumptions on the drift, we show that there is a unique solution, which has moments of all orders. We also apply the techniques of Malliavin calculus to prove that the solution has an absolutely continuous law at any time t>0t>0.