Zadi, Noureddine LanjriNualart, David2015-03-112015-03-112003-07-25Zadi, Noureddine Lanjri & Nualart, David. "Smoothness of the law of the supremum of the fractional Brownian motion." Electronic Communications in Probability. (2003) Vol 8. pp. 102-111. http://dx.doi.org/10.1214/ECP.v8-1079.https://hdl.handle.net/1808/17050This is the published version, also available here: http://dx.doi.org/10.1214/ECP.v8-1079.This note is devoted to prove that the supremum of a fractional Brownian motion with Hurst parameter H∈(0,1) has an infinitely differentiable density on (0,∞). The proof of this result is based on the techniques of the Malliavin calculus.Malliavin calculusfractional Brownian motionfractional calculusArticle10.1214/ECP.v8-1079openAccess