This note is devoted to prove that the supremum of a fractional Brownian motion with Hurst parameter $H\in \left( 0,1\right)$ has an infinitely differentiable density on $\left( 0,\infty \right)$. The proof of this result is based on the techniques of the Malliavin calculus.
"Smoothness of the law of the supremum of the fractional Brownian motion." Electron. Commun. Probab. 8 102 - 111, 2003. https://doi.org/10.1214/ECP.v8-1079