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

Zadi, Noureddine Lanjri; Nualart, David

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Issue Date

2003-07-25

Author

Zadi, Noureddine Lanjri

Nualart, David

Publisher

Institute of Mathematical Statistics

Type

Article

Article Version

Scholarly/refereed, publisher version

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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.

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.

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