From forward integrals to Wick-It\^o integrals: the fractional Brownian motion and the Rosenblatt process cases
Probability
2017-01-03 v1
Abstract
In this paper, we combine Hida distribution theory and Sobolev-Watanabe-Kree spaces in order to study finely the link between forward integrals obtained by regularization and Wick-It\^o integrals with respect to fractional Brownian motion and the Rosenblatt process. The new methodology developed in this paper allows to retrieve results for fractional Brownian motion and to obtain new results regarding the Rosenblatt process. In particular, an It\^o formula for functionals of the Rosenblatt process is obtained which holds in the space of square-integrable random variables.
Keywords
Cite
@article{arxiv.1701.00129,
title = {From forward integrals to Wick-It\^o integrals: the fractional Brownian motion and the Rosenblatt process cases},
author = {Benjamin Arras},
journal= {arXiv preprint arXiv:1701.00129},
year = {2017}
}
Comments
32 pages