Smoothness of the law of the supremum of the fractional Brownian motion

Abstract

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. © 2003 Association for Symbolic Logic.