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

Noureddine Lanjri Zaïdi (Université Ibn Tofaïl, Kénitra, Maroc)
David Nualart (Universitat de Barcelona)

Abstract


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.

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Pages: 102-111

Publication Date: September 15, 2003

DOI: 10.1214/ECP.v8-1079

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