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Smoothness of the law of the supremum of the fractional Brownian motion
Zadi, Noureddine Lanjri Nualart, David
Zadi, Noureddine Lanjri
Nualart, David
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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.
Description
This is the published version, also available here: http://dx.doi.org/10.1214/ECP.v8-1079.
Date
2003-07-25
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Institute of Mathematical Statistics
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Keywords
Malliavin calculus, fractional Brownian motion, fractional calculus
Citation
Zadi, 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.