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.
|Journal||Journal of Mathematical Analysis and Applications|
|Publication status||Published - 15 Jun 2007|
- Fractional Brownian motion
- Fractional Sobolev spaces
- Wiener integral