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

By M. Jolis. 2007

70 citations recorded by the source corpus.

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 W 1 / 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 .

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4410942ea2cf0625a2bb4c83fce20baf269b2798

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. P. Lei
2. David Nualart

In Finance

1. P. Lei
2. David Nualart
3. Ivan Nourdin
4. Giovanni Peccati
5. Frederi G. Viens
6. Ciprian A. Tudor
7. Christian Bender
8. Yaozhong Hu

In Mathematical Physics

1. P. Lei
2. David Nualart
3. Ciprian A. Tudor
4. Khoa Le
5. Frederi G. Viens

Citations in the corpus

• A decomposition of the bifractional Brownian motion and some applications (2008, background): “In a recent work, Jolis [4] has proved that if H > 1 2 , the space HBH is the set of restrictions to the space of smooth functions D(0, T ) of the distributions of W 1/2−H,2(R) with support contained in [0, T ].”
• Wiener integrals, Malliavin calculus and covariance measure structure (2006, unknown): “Among the most recent references there are [33] for the case of fractional Brownian motion and [20] when X is a second order process.”