On the Wiener integral with respect to the fractional Brownian motion on an interval

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Abstract

We characterize the domain of the Wiener integral with respect to the fractional Brownian motion of any Hurst parameter H ∈ (0, 1) on an interval [0, T]. The domain is the set of restrictions to D ((0, T)) of the distributions of W1 / 2 - H, 2 (R) with support contained in [0, T]. In the case H ≤ 1 / 2 any element of the domain is given by a function, but in the case H > 1 / 2 this space contains distributions that are not given by functions. The techniques used in the proofs involve distribution theory and Fourier analysis, and allow to study simultaneously both cases H < 1 / 2 and H > 1 / 2. © 2006 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)1115-1127
JournalJournal of Mathematical Analysis and Applications
Volume330
DOIs
Publication statusPublished - 15 Jun 2007

Keywords

  • Fractional Brownian motion
  • Fractional Sobolev spaces
  • Wiener integral

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